We just took a trip to Wally World up the street, and while there....she latched onto a Daisy brand wrist-rocket, some slingshot ammo, and some high-velocity airsoft rounds.
I’ll let ya know if the whole slingshot approach works. If so, I’ll probably spring for the fancy Wrist Rocket Pro (above).
Unless you're in a hurry to get rid of the squirrels, then I wish that, er, uh...
Anyway, have loads of fun and be safe, and please do let us know how it goes.