Wrist-rockets will definitely kill small game. Killed a grouse with one once, had a nice meal while backpacking.
Buy more 22 ammo and if ones wants quite us CBcaps or the new CCI quite 22.
Marbles make great ammo for a Whammo or wrist rocket. Easily takes rabbits or squirrels without neighbors or home owners assoc. knowing a thing. My garden is one of the few in my area without a rabbit problem. Dogs and cats seem to stay out of my yard for some reason also.