I don't know that I would find a use for the derringer, but I use .22 Short for squirrels and 'quiet' plinking.
It doesn't take much power to kill a squirrel. .22 Short, .22 Long, or .22 LR... it doesn't really matter. But....
With .22 LR, I can fit 12 rounds in my Winchester 62 clone. With .22 Short, I can fit 19. One of my brothers has a Browning BL-22 that will hold something like 23 rounds of .22 Short.
Load it on Sunday, and shoot all week...
"Such is the strange way that man works -- first he virtually destroys a species and then does everything in his power to restore it."