Call of Duty: Black Ops
Unless it's extreme circumstances, you can't get banned in Singleplayer.
Only using it in multiplayer will you get banned for it. Even if it does work, since it's usally a different .exe for CoD multi.
So cheat in SP. Don't cheat in MP.
(Plus, the trainer is only really designed for SP use!!)
VAC2 is nothing more than a quick scan of your memory (RAM) to see if any variable change is applied to the normal gameplay. This does not apply to SP mode. The file you have found for the vac_0 or whatever is nothing to be afraid of. Valve would never put a vac2 file in your computer to make it "obvious".