The only critters I send to a better place are groundhogs.   
My home is built on stilts, and those ba%$#^&ds dig holes all around the foundation, and have gotten under the house, chewing wiring, tearing up insulation and such. 
  I live in the country, so I use a mini 14 to do the deed. 
  If you live in an area where you're not allowed to discharge a firearm,  they do make subsonic .22 rounds that are pretty quiet, and very effective on something as small as a squirrel. 
  They're a bit more expensive, and not intended for target shooting, but rather for just the sort of problem you're having.   
  Happy hunting.