We had the same issue with skunks getting under our house, did some research and found that taking some rags and pouring ammonia on them then leaving the rags around were the skunks go would get rid of them, the ammonia makes them think there is a fox around and they leave, it worked for us, no more skunks under the house.
How to get rid of a skunk? You vote them out of office
I was watching the exterminators TV show and the guy caught one in a have a heart trap. He had to approach it with a tarp to keep from getting sprayed when he grabbed the cage, he got nailed a little. If you don't want the stench I would say a head shot with a good pellet gun is a lot more humane than letting it starve to death trapped in a cage. I wouldn[t poison it. It will surely die under the pool, how fun would that be?
What traps are you using? Live or foothold/body gripping (instant kill)? If instant kill is it big enough? Under your porch or just wandering around? When I was trapping I'd catch them in footholds. The method I used for removing them was a pole with a hypodermic needle on top and fill with acetone about 10cc's and I used my 4' hoe). Then just talked quietly to the skunk as crouching and approaching slowly. If it stomped its front paws or turned its butt towards me I backed off. When got close I'd let it sniff the hypo. and when it was okay with it I'd put it right behind the shoulder and push in gently. Couple times I actually pushed the skunk over doing this but it was relaxed from doing the above first. With needle in would push to push the plunger down and then pull out and back off. Usually within 20 seconds the skunk would just yawn and lay down and die. Then would usually put a few more cc's in and inject again just to be on the safe side. Skunks are effected very easily by anesthesia. Using this method had 4 skunks in my trunk once and skinned 3 in the basement. Fourth thought could just smell a bit so did it outside.
Others say shooting behind the shoulder with a .22 but I never did that. Others say grabbing by the tail and lifting the hind legs it can't spray but I'm not going to try it.
If using live trap then would talk gently and place blanket over it and then put in pickup bed or trailer and take someplace and open door.