A blaster pistol is used by the Mandalorian aka Dyn Jarren (Pedro Pascal) as his main sidearm. It is based on the Bergmann 1894; because of the rarity of the real pistol, it seems likely that the prop used in the show is a replica instead of an actual Bergmann 1894. A number of modifications were made to the Bergmann 1894 for the blaster's design, including new iron sights, a muzzle device, a modified grip, a modified hammer, and a smoothed out magazine cover with the circular grasping handle removed.
A drill bit substitutes the cleaning rod on the side of the gun, likely due to the prop being a replica.
BlasTech DH-17 Blaster Pistol (Sterling SMG)
The BlasTech DH-17 Blaster Pistol, based on the Sterling SMG, is used by some Mandalorians backing up the Mandalorian at the end of "Chapter 3: The Sin". In "Chapter 6: The Prisoner", New Republic Security Droids use the DH-17 as their primary weapon, then the Mandalorian uses it to bust of a jail cell.
BlasTech SE-14C Blaster Pistol (Rexim-Favor Mk5)
The Rexim-Favor Mk5-based "BlasTech SE-14C" is used by Remnant Stormtroopers as their sidearm.
Ruger Mk II
A suppressed Ruger Mk II is seen with a Rodian-type Guild bounty hunter in "Chapter 3: The Sin".
Rodian DT-12 (Ruger Mk III)
Mayfeld (Bill Burr) is seen using the "Rodian DT-12" blaster pistol, a heavily-modified Ruger Mk III.
A highly modified Astra 400 appears in the Mandalorian's Arsenal, and is later one of the weapons used to arm the farmers in "Chapter 4: Sanctuary". An identical pistol is also carried by one of the guild bounty hunter in "Chapter 3: The Sin". Mayfeld (Bill Burr) is also seen using the same model in "Chapter 6: The Prisoner".
Accles & Shelvoke Acvoke
An Accles & Shelvoke Acvoke air pistol fitted with wooden grips and a reversed M38 azimuth telescope on the right side can be seen in the Mandalorian's arsenal. This is also one of the weapons which he uses to arm farmers with in "Chapter 4: Sanctuary".
Apache Fireball Air Pistol
An Apache Fireball Air Pistol fitted with a ribbed barrel shroud is in the Mandalorian's arsenal, and is also one of the weapons he uses to arm the farmers in "Chapter 4: Sanctuary".
Webley Tempest Air Pistol
A Webley Tempest Air Pistol modified with a wider and longer barrel appears in the Mandalorian's arsenal. It is also used by at least one of the guild bounty hunters in "Chapter 3: The Sin". Toro Calican (Jake Cannavale) carries this pistol fitted with a scope (the same M38 azimuth telescope seen on many Star Wars weapons) and a cone shaped muzzle device in "Chapter 5: The Gunslinger".
Webley Premier Air Pistol
A heavily modified Webley Premier Air Pistol is used by Mayfeld (Bill Burr) in "Chapter 6: The Prisoner". The pistol has had the original barrel entirely removed and instead the piston tube portrays the barrel and is fitted with a cone shaped muzzle. A block has been fitted ahead of the rear sight to hide the original now empty breech area, and what appears to be an aiming laser is fitted above the muzzle. Based on the number of trigger pins and the rounded washer-like sections at the bottom of the barrel locking latch, this appears to be a Model E variant of the pistol.
A180 Pistol (WE Luger P08)
Davan (Matt Lanter) uses an A180 pistol, which was based on a Luger P08. This pistol appears to have been built up from an airsoft (6" barrel) WE Luger with a large barrel shroud (reminiscent of the LPA NN-14's from The Force Awakens). The Luger's rear sight has also been removed and the "tab" behind the rear sight ground flat.
Steyr M1912
In "Chapter 3: The Sin", Greef Karga (Carl Weathers) uses a blaster pistol based around a Steyr M1912.
DL-21 (Charter Arms Explorer II)
A Charter Arms Explorer II modified with a scope and a thicker barrel with the tail section from a British 2 inch mortar shell on the muzzle appears in the Mandalorian's arsenal. This blaster model is known as the DL-21 and despite being little seen or known actually appears in all three original trilogy films to some degree. The original prop was a cut down Armalite AR-7 using a either a modified Sterling SMG grip or a simple rubberised rod of some sort.
A Webley & Scott No. 4 Mk. I with a collar on the barrel is one of the weapons in the Mandelorian's arsenal. This is also one of the weapons that is picked up and examined by Cara Dune (Gina Carano) in "Chapter 7: The Reckoning".
Unknown
Blaster Rifles
Amban sniper rifle
The Amban sniper rifle is used by the Mandalorian as his primary weapon. In "Chapter 4: Sanctuary", Cara borrows it from the Mandalorian and uses it to good effect. In some of the original concept art for the series, the rifle was built off of an AKM receiver. However, the actual rifle used appears to be an entirely fabricated prop.
Beretta M12
A Beretta M12-based blaster rifle is seen with armed characters in the season.
BlasTech E-11 Blaster Rifle (Sterling SMG)
The BlasTech E-11 Blaster Rifle, based on an airsoft Sterling SMG, is used by IG-11 as one of its weapons in "Chapter 1". Remnant Stormtroopers use them as their main rifle, sometimes outfitted with tac lights.
Bren Mk1
In promotional images, Cara can be seen using a modified Bren Mk1. The original magazine well has been covered over and instead a double drum from an MG34 is fitted to the bottom of the receiver, and a second barrel has been mounted in place of the gas piston tube. The same weapon can also been seen in the Mandalorian's arsenal in "Chapter 1".
E-22 Blaster Rifle (Sterling SMG)
In "Chapter 3: The Sin", one of the Remnant Stormtroopers uses what appears to be an E22 Blaster rifle, as seen in Rogue One, this one outfitted with a tac light. These blasters are also based on airsoft Sterling SMGs, like the E-11.
Defense Technologies 37mm Gas Gun
The Defense Technologies 37mm Gas Gun is seen in the show as modded for laser rifles. They appear in several episodes being carried by various background characters along with being present in the Mandalorian's arsenal. They are also the standard weapon carried by a group of Death Watch Mandalorians during a Clone Wars era flashback in "Chapter 8: Redemption".
A Relby V10 Targeting Rifle appears in the Mandalorian's Arsenal in "Chapter 1". The same weapon appears in "Chapter 4: Sanctuary", where the Mandolorian gives it to Omera (Julia Jones) who uses it to great effect during the battle against the Klatooinian raiders. This blaster is based around a Schermuly Multi-Purpose Gun fitted with twin Sherman Tank gunsights. This blaster was previously seen in the hands of Bossk in The Empire Strikes Back.
Federal Gas Riot Gun
A Federal Gas Riot Gun modded as a blaster rifle is one of the weapons in the Mandalorian's arsenal which is used by a villager in "Chapter 4: The Sanctuary". This is also one of the weapons that is picked up and examined by Cara Dune (Gina Carano) in "Chapter 7: The Reckoning".
Dragunov SVD
In Episode 5, mercenary assassin Fennec Shrand (Ming-Na Wen) is seen using a scoped blaster rifle based around a SVD Dragunov (or, more likely, an airsoft replica thereof).
Ottoman Musket
Tusken Raider are seen with an Ottoman-pattern musket; unlike many other weapons in the series, this one seems more or less completely unaltered, possibly being meant as an actual projectile-firing musket (which the Tuskens are noted to use in some lore sources).
EE-3 Carbine Rifle (Webley & Scott Flare Gun)
The droid bounty hunter Zero (voiced by Richard Ayoade) carries an EE-3 carbine rifle in "Chapter 6: The Prisoner". The EE-3 is built from a Webley No. 1 Mark 1 flare gun that has been fitted with a finned barrel shroud and a scope. This is the variant of the EE-3 that was previously seen in Return of the Jedi (and the special edition version of A New Hope) as opposed to the simpler variant from The Empire Strikes Back.
Unknown
Special Weapons
Flamethrower
A flamethrower is seen with the Mandalorian mounted on his wrist gloves.
Mini-Missile Launcher
A mini-missile launcher is seen with the Mandalorian mounted on his wrist gloves.
Heavy Weapons
Fictional Heavy Blaster
A handheld Minigun-styled blaster machine gun is seen in "Chapter 3: The Sin" with Mandalorian fighter Paz Vizla (Tait Fletcher). The receiver appears to be based on an enlarged MG42 receiver and near section of the barrel shroud, whilst the three barrels are styled on MG34 barrels.
M61 Vulcan
A M61 Vulcan-based blaster machine gun is seen in "Chapter 1" when armed crooks take on the Mandalorian and the IG-11.
Others
Razor Crest Arsenal
The Mandalorian has an arsenal of small arms inside the Razor Crest. Almost all of them are actual firearms that are modified to give them a sci-fi appearance. Most (if not all) of these are used by villagers in "Chapter 4: Sanctuary".
Jawa Small Arms
The Mandalorian encounters a bunch of unhappy Jawas armed with small weapons in "Chapter 2: The Child".