If the muzzle blast upsetting the neighbors is no problem, the .223 would work just fine.
Cartridges like the .22 Hornet and the .218 Bee were quite common for shooting groundhogs in the smaller farms of Pennsylvania. An equivalent cartridge, today, is the .17 HMR. I'd call them 150-yard cartridges, insofar as a clean kill.
Then came the .222, which extended the range but still wasn't all that loud. The .223 is basically a .222 Magnum, but with a shorter case neck.
You're from BATFE? Come right in! I use all your fine products!