I have caught many skunks in a live trap and none of them sprayed when the trap closed (too busy eating the bait) and none of them sprayed as I approached the trap.
If the shot is placed correctly, the skunk will not spray. What will happen is that all of the sphincter muscles will relax with death allowing the scent glands to discharge but it will not be as a spray.
In most places it is illegal to relocate skunks, fox, opossums, raccoons, etc.
I shoot them in the trap and bury them as quickly as possible. A solution of bleach and water will help get rid of the smell.