Old beekeeper trick. Take a raw egg and punch a hole in one end if it. Take three aspirin, powder them up, and mix them into the egg. Make sure it's well blended. Dig a hole the size of the egg and place the egg in it with just the open end showing.
The aspirin acts as an anticoagulant. Skunk wanders off and then falls asleep forever.
The amount of aspirin is enough to kill the skunk, but not enough to bother a dog. Cat's will usually leave it alone.
And if they die under your house?
