Our neighbor is borrowing the Havahart (that's the kind of trap that is, they're great) and trapping a fair amount of "game" so I just have to run around at night chasing down funny noises to find the critters myself. We've trapped a lot of possums, the occasional coon, no skunks recently that I know of.
Shooting possums, well, they can take a LOT of pellets without dying (right away at least), as I verified again tonight with two possums in a tree. Dispatching them in the trap, so the shots are point-blank, I can tell you, pellets have almost no effect. CB Longs/Shorts, being solid round-nose bullets, seem to have little effect also. Remington Subsonics, which are not like Colibris, by Subsonic they mean standard velocity, 800-900 fps or so, hollow-point, do the job. But I'm extremely leery of shooting something like that up into a tree. I need to get off my dead butt and work out a way to put a hollow point into a CB Short/Long bullet, because then it will expand and may be a lot more effective. The Remington Subsonics make a little noise, the CB's are very quiet, out of a rifle barrel.
For the OP's situation, I recommend getting a Havahart trap and trapping the critters, then disposing of them. Since they're skunks, I don't know what to suggest for dealing with the stink.