I had one in .22wmr once upon a time... wish I still had it. The .22wmr seemed to me to be just fine for the intended use...
The Hi-Standard 22 LR semi-auto is a really accurate firearm. Used to train OSS back in the day, and then later models well into the 60’s. But... they are not small like a close in derringer.
Alternatively, a Walther 380 with special rounds is small and quite deadly close in.