Galting is 100% right. However nothing stops you from trying, at least to have fun. Like Gatling said, small guns crippler builds are your best option (10 luck, Finesse, Better Criticals, 3xMore Critical). You could make a shared tent with all your partners and start gathering cheap guns (I don't recommend Shotguns since shoot-twice-and-reload is not so good for PvP in real time). Try organizing quick trading operations with NPC gun merchants with 1 Charisma requirement (try New Adytum, Gecko, New Reno, see
here - although New Reno might be dangerous), you can simply craft and sell BB's from Junk in nearby urban areas, which will make guns almost free. Or just craft a shitload of BB guns and BB ammo, which can still cripple your enemies, and can be crafted even by powerbuilds. Either way do some patrols around the wasteland, wearing no armor. Yeah, one could say this would be almost like trolling, but the cause is just!
The only problem I see with all this, is when you actually go the where a distress call has been sent from, and you have to know who's the PK and who's the victim shooting in self defense. But if you stick to the NCR area, this will tend to be not so difficult to know I guess.
Also, bluesuit + BB gun guys might not exactly look like members of a Police Department, but rather some sort of weak and cheap guerrilla. But well you can't have everything

Hope you enjoy!