Like most animals, yes, kittens and puppies will be destructive, claw and knaw, and have to be told what is not allowed. Cats and dogs are pack animals, skunks more solitary. They are more active, exploring, into everything, and I think it is their nature to have a den to sleep in, a safe place.
Like other little kids it needs to be loved, taught, and have toys. As mother you should lick it's face clean often. OK, you can use a damp sponge, but grooming is a close bond, and expected.
You have to get it used to being handeled while young. I am not sure where, but they fit with bears and woverines, badgers, and can hold their own. You want to be friends.
They do like to dig, and a den in the yard, stacked bricks, throw some dirt over, a center room with several exits, just skunk size. The females are more house loving, males wander more. The more you fit into their world the more they will join in yours.
Mimic sounds and movments, it makes you look real. It would help if you watched and listened to mom skunk, learned a bit, how to call, come, stop that, scolding, danger, and watch grooming, for you will be replacing mom. The young need a lot of body contact, like a kitten in a safe lap. They grow through that stage quickly, but the bonds last.
It is not just a fur ball, there is a personality there. I take kittens out on their first hunt, in foot high grass, it is an adventure. I stalk grasshoppers. I go out with the dog at night, all around the house, looking under cars, under the house, inspecting the cats, and the dog does it when I am not around. So on hands and knees teaching your skunk child to hunt bugs and worms.
The idea is establishing yourself as hunt leader, and that lasts.
It will also take on your personality, so set a good example.