A 38 or 44 shot shell going off will sound as loud as a 2 1/2" shell in a .410 shotgun. Been there done that.
Best way to get rid of squirrels in the city, close to neighbors, is to get one of the "live traps" that is open at both ends. Catch them and relocate them -- release five miles or so from your office. Google Havaheart traps if interested.
A pump 22 caliber pellet gun would be your next best solution. Just three or four pumps is enough and is fairly quite. The "adult" break action pellet guns are loud and more than you need.
A 12-gage shotgun with #6 shot gives really personally satisfying results for the da** pests, but that does not work so well with close neighbors.
