You could get a live trap and put a bowl of cat or dog food on the switch that sets the trap off. Even then you still have a live skunk on your hands. You need to be careful they can spray up to 40 feet. Also, if you kill it there might be fines or something if you have already reported a skunk being there.
I'd recommend tying a really long rope onto the live trap so you can halfway cart the thing off at a good long distance and not get sprayed.
The way my dad sometimes had to take care of them when they got in our barns was to gas them to get them to fall asleep, basically knock them out. Then you can remove them without the worry of getting sprayed. However, this is your house, so if you did something like that you wouldn't be able to stay in your house till you aired it completely out.
Animal control or the DNR might be your best bet. As long as you don't bother him or don't scare him, he shouldn't spray you.
You absolutely don't want to get sprayed.
Probably your best course of action is to lure the skunk outside with a bowl of cat or dog food late at nigh. Then while one of you has the skunk spotted outside. Another person should go into the basement and close up the door from the inside. The next day or so when the skunk isn't around spread some dog or coyote urine around the area, the smell of a predator might scare the skunk away.