I'd think a decent .22LR at fairly close range through the head would do the trick, but wouldn't want to risk it in my house/car. Cut the spinal cord/brain intersect & things don't happen any more. Don't & things just might ....
Reason I mention car is one day, I fired up my Land Cruiser, got all set to go & opened up the glove compartment. Inside sat a youngster striped skunk.
First thought was to, well actually - run!, second was shoot it. That thought lasted a whole second or two for obvious reasons. Shooting a skunk & putting a bullet through it AND the firewall didn't seem too good an idea.
I decided to just close the gc door and drive on, hoping for no smells .... Got to work, called the DOW. They said mothballs will keep 'em out & away - they didn't. Ended up (gently) poking the poor little fellow with a straightened out coathanger for about an hour till he finally left the scene. A cute li'l fellow & never did act nasty in any way. Kinda hated to see him go, except for the potential for absolutely ruining my LC.
Was driving once & the car in front of us dusted a skunk. Stopped to take a look. Looked like the skunk had no damage whatsoever & always thought a skunk hat would look cool. This thing had absoolutely no smell - you could literally stuff it into your nose & take a big ol' huff. Cool for me ....
Skinned it & since I wasn't going to be able to tan it right away, I ziplocked it & pitched it into the freezer. Next day, the entire refrig's contents (& I mean everything! stuff in jars not even opend yet) were permeated with the smell ... bad idea.
BTW, if your cat gets skunked, a bath with tomato juice gets you scratched & makes the tub area look like Manson's been visiting ...