Back to the OP's question about using a bore snake to clean a .22 handgun. Yes, I too like bore snakes for cleaning handguns. With only 2" to 6" of barrel length, they work well. With CLP they do a fine job cleaning revolvers & semiauto handguns from .22 to .45 caliber.
Probably, you will eventually have to do some lead cleaning with solvent, brushes & patches. Depending on how much you shoot, it could be an annual chore or even several years between that level of cleaning. I've bought a few older, used .22's that had probably never been cleaned and it didn't take long to get the bores cleaned up. And for a plinking .22 handgun, you won't hurt anybody if you always just use a bore snake to clean.