Bon Bon from my Fic I'm writing, if your curious, no the weapons do not have triggers like humans do, they have similar mechanisms but the little details change how it fires to accommodate the lack of fingers.
I had the same issue while thinking in the trigger. Maybe they have the weapons hanging at one side of her body (like in your drawing) and they move and press a button that acts like a trigger for the weapon.
I've classified the types in my fic, Lever action/Pump(instead of it just putting a new shell/bullet in, it fires one too.) BRB(Big Red Button), shoulder mounted, and magic fired(unique unicorn weapons)