Two Methods of Skinning.
There are two distinct methods of skinning fur-bearing animals, and skins are known as "cased" or "open" skins, according to the method of removing the pelt. Open skins are those removed by ripping the skin down the belly and are stretched out flat. Cased skins are those drawn off the body from the tail to the head, by ripping the skin on the backs of the hind legs.
The skunk skins should be cased. Cut off the front feet with a knife or hatchet, cut around the hind feet and rip down the back of the hind legs, using care when cutting and skinning around the scent glands. Split the tail about one-third of its length on the under side, and skin it that far by using the knife; then strip it from the bone by means of a split stick. Grasp the stick with your right hand, palm up, and with the tail between the second and third fingers, tail pointing up; hold the carcass by placing the left hand on the hind quarters; close your right hand and give a steady pull upwards and the skin will be stripped from the tail quickly and easily. Now draw the skin downward, off the body, to the shoulders. Here two thin muscles will insist on hanging fast to the skin; put your finger under them and tear them loose. You can now get hold of the front legs, and strip the skin from them. Strip the skin on down to the head, then feel for the base of the ears and cut them off close to the head. Skin on to the eyes; here you must use the knife again, but use care not to enlarge the eye aperture. Cut the skin loose about the mouth and the end of the nose, but don't cut the nose off the skin. The pelt now resembles a small, narrow sack, with fur side in. Before you lay it down, turn it with the fur side out and thus keep the skin clean until you are ready to flesh and stretch it.