Varmit shooting I've done a bit of.
Used to have REALLY big wharf rats swim up a river, and eat garbage from our garbage area, restaurant fed rats.
First we tried a high velocity .22 pellet gun, at 950 fps. Looked like one of those break, pump rifles shown earlier in the thread. I hit mama rat, at about 8 feet, with a shoulder shot. Didn't penetrate, and, she looked at me, angry as hell.
My other choice was to shoot her with a Detonics Mark VI, in 45 Super I was carrying, but, I don't think that would have gone over well with the rest of our bunny hugging staff.
Next, we moved up to 22 short. CCI Hollow points that didn't open up. IIRC. They went 6-8 inches in big rats, and, they didn't move much. Humane kill. That out of a 22lr rifle, with 18 inch barrel.
For varmits, etc. I'd suggest a CZ 452. Super accurate, and cheap. It's in 22lr, but will single shot in 22 short, with an excellent scope on it, it will drive tacks at 25 yards, like under a 1/4 inch.
You can also use 22lr in it, with sufficent bullet weight to do in varmits.
That said, I'd figure out a way to spray the skunk, so you don't have to kill em.
I'm sure there is some way to do so. I just had the s... scared out of me by another thread about some worm in racoons, that might spread.
Look for some threads on humane skunk control. Cut little guys, that, in the proper setting, make really fun pets. Smart, cute, and desmelled, only slightly worse at tearing up your house then our half