It's more about the size of the shot than the gauge used. Only ever used 4's out of a 12 gauge myself. Modified choke, I think. It's been a while. 4's out of a modified 12 do not blow a tree rat into a mist either. There is no such thing as "not overly loud" with any shotgun.
"...If you're not going to eat the squirrels..." Violates hunting regs to waste game meat. Depends on where you are, of course, but tree rats are considered game animals in most places. Make absolutely sure of their status first. It's easier and less expensive to remove food sources and den/nesting sites plus spreading blood meal around, both of which are entirely silent.
"...If you're not going to eat the squirrels..." Violates hunting regs to waste game meat. Depends on where you are, of course, but tree rats are considered game animals in most places. Make absolutely sure of their status first. It's easier and less expensive to remove food sources and den/nesting sites plus spreading blood meal around, both of which are entirely silent.