Yeah I was thinking a light pistol with a custom stock, grip and forehandle would work.
A heavy pistol's recoil would knock that little flying insect onto it's back and down the hall!
Flying characters and guns in general shouldn't work out well.
But yeah a small pistol with tiny combat grip, tiny shoulder stock, fired with both hands would be feasible. Getting a functioning hand gun down to doll sized is possible. Breach loaded .22s aren't much more than 3 inches long. Wildly inaccurate, only holds one or two shots, small caliber, and you're not sticking any kind of fancy high tech high velocity rounds in a weapon that small. But yeah, think .22 Derringer, and it's still going to be about as long as a Pixie's forearm.
Also, keep in mind some of the larger magazines are going to be as long as a Pixie's leg. All very silly.
Either be a Pixie mage or a go Monowhip.