Surprise. But you also don't have to handle just GUNS to be an armorer. I've known many SWORD and edged weapons 'armorers' who worked on 'Robin Hood" and other Medieval period adventure movies. They're in charge of all swords (real, combat, stunt, rubber, decorative, etc) and other items like crossbows, arrows, melee weapons, etc.
Again, there is crossover there, since many films also call the person in charge of designing, building or providing the ARMOR worn (plate and chain by King Arthur's knights, for example) as an armorer. In those epics, an armorer might be the guy providing ALL of the armaments, even the armor worn by the actors and stunt performers, or sometimes JUST the weapons.
On films like Last of the Mohicans and The Patriot (2000), all of the weapons were flintlocks. The master armorers didn't need to have FFLs and certainly weren't NFA licensed (they didn't need to be). All the assistant armorers were just trained assistants who knew how to safely load, fix, clean and secure black powder weapons for the movies.
Just more ramblings.