There's really only 3 weapons that are staples in Mando culture. Beskad which are swords, Besk'bev which is a flute that can be used as a club or spear, and the Mythosaur Ax used by the ancient Mandalorians. As far as guns go, we can only really say that the Verpin Shatter Riffle was used a lot (but not necessarily exclusively) by the Mandos since at least 40bby. Crushgaunts are also a "mando only" weapon, but were outlawed both by the republic and later by a Mand'alor looking to bring the mandos back into a more "moral" light.
Mandos use whatever they can get their hands on, even if they aren't proficient with it. There are no "Mandalorian" specific manufactures, and every race that's interwoven themselves into the Mando culture has brought some sort of weapons technology to the culture. So in a sense, any weapon could be a mandalorian used weapon.