One of the caretakers that i know was having a squirrel problem. He said that .22 cal rat shot worked pretty well. I used to use the kind with the crimped brass ends ages ago and had spent shell ejection problems but the new kind has a plastic end.

I think i would be more likely to put out D-Con rat baits around the property. We've been using it here for mice for decades. Does a bang up job and you don't have to fuss with the traps.

The Have a Heart rat traps can be fun. You live catch .... from there you just relocate them to somewhere else. Maybe your neighbor's trash can ?