That really stinks, pun intended.
I've lived in several places in which skunks were a real serious problem, both as a stinky menace, and also because my dog would be constantly getting sprayed. My worse problem was when i lived up in N. Arizona, the skunks would come into my back yard every single night, so I decided to start shooting them. But as it turned out, skunks aren't as easy to shoot as I thought. they are crafty and seemingly smart, and can smell our scent which sends them running off.
So I started out using my bow, mostly because it was quiet, thus my neighbors wouldn't be alerted to my activities. the bow was very effective, but the problem was that the skunks wouldn't die instantly, often spraying very heavy which would only cause more stinky problems for everyone, neighbors included.
So my next thought was to use a good pellet gun, which at the time the only one i had was an inexpensive Daisy 10 pump. Anyway, I put a scope on it, kept my back yard light on, but with a low watt bulb, just in case it would discourage them from visiting my yard.
The first night one came into my yard, so I put the cross hairs on his head, "pop", he rolled over and died nearly instantly, best part he didn't spray at all. This went on for a few days, one after the other, head shots, none spraying either. After a good 10 or 12 skunks over the course of a couple weeks, I stopped being bombarded by them, just an occasional one or two for the rest of summer. By next summer they were back in numbers once again, and I got rid of them once again.
So if this story has a message, it would be three.
1. Make sure they die instantly, head shots are the trick I think.
2. Make sure you have some place to discard the carcass, and make sure they aren't easily accessible to other animals, as skunks are known to carry rabies, and this would be a sure fire way to start an epidemic, IMO. I took them to the woods, dug a deep hole, buried them, then put a bunch of large boulders on top to prevent coyotes and other scavengers from getting to them. Seems like a lot of work, but rabies are nothing to take chances with regard to starting an epidemic. Once the animal / brain has been dead a couple days or so, the risk is no longer present.
Be careful when handling them. Getting blood on an open cut, or into a membrane such as the eye's, mouth, nose, or accidentally scratching yourself on a tooth can infect you. I once had a very scary incident when I broke the skin on a coyote tooth while skinning it. County animal control submitted it to the county health dept. to analyze the brain. Thankfully it wasn't infected.
GS