Skunks and people each have their own habitats, and it's always best to keep them separate. For moral and practical reasons, killing a skunk is not a great idea. Getting rid of a dead skunk is a project in itself. Catching one, and transporting it to an appropriate skunk habitat, without getting sprayed, is the desirable outcome – a win-win for you and the skunk. It's easier than you might think to prevent spraying. You just have to prevent the skunk from raising her tail. This means building a standard DIY live-rabbit trap, with special dimensions.
One of the 24 inch long pieces of wood is your top. Drill or cut two 1-inch holes, centerline, six inches from each end. Screw the 2 x 4 onto the top board, pointing up, with the long side corresponding to the long axis of the top. It should stick up like a shark's fin. Attach it halfway between the two holes, but laterally set off so the edge of the 2 x 4 is 3/16 inch from the longitudinal center line. This leaves room for your yardstick lever. With the trip mount attached to the top board, you can put the box together.
Screw the sides, top, and bottom together to form your "box tube." All pieces are equal, so there is no wrong side, top, or bottom. Fit the pieces so they overlap clockwise or counterclockwise, and fasten each joint with four wood screws, through the side of the top board through the end of the bottom. You will have a 24-inch long square tube, with a 6-inch by 6-inch channel. Pick an end to be the back, and screw on the 6 3/4-inch by 6 3/4-inch back with four screws. Metal cloth is optional for added ventilation. Screw the hinge into the door. Place the attached hinge at the top of the remaining aperture, so the door will open inward and swing down to close. Screw the hinge in. Screw the drawer handles onto the box at opposite corners on each end. When you pick up the box by the handles, the box should be lateral across the front of your body. These critters will wiggle when you pick up the box.
Screw the eye-screw into the door, 1/2 inch from the bottom edge, inside face, dead center. Cut a piece of aluminum diagonally from a used can, 1/2 inch wide and at least 5 inches long, longer if possible. Punch a small hole in one end. Cut the yardstick neatly at 12 inches long. Drill a 3/16-inch hole, centerline, exactly 6 inches from either end. Drill two more holes exactly 3/4 inch from either end. Screw the yardstick arm through the center hole into the side of the 2 x 4 "shark fin," near the very top. It should see-saw easily there. If not, loosen the screw a bit. Tie the monofilament line to each end hole on the yardstick arm. Tie the door-end line to the eye-screw in the door, passing through the hole in the top of the box. Once tied, test the length of the tie. Push down gently on the yardstick arm until the door is completely raised inside the box. Chock the arm into this position. Tie the trigger end line to the aluminum strip, so the strip goes into the back hole with only an inch or so left outside the box. Fold the trigger with your finger so that it grabs the anterior lip of the hole and holds up the door, then fold the rest of the tail toward the back of the box. It should lightly drag the "floor." Unchock and test. When the animal heads to the back of the box for the bait – salted bacon is best – it will push the aluminum trigger off the lip and allow the door to fall closed behind the critter.
Skunks cannot raise their tails in a 6 x 6-inch space. You have a sprayless box trap.