For real the best way is to slowly walk up holding an old blanket between you and the skunk in the cage then throw the blanket over the cage.
Then you can take it to wherever you are going to release it - preferably in the back of a truck.
Then you can release the trap with the blanket still over the cage and walk away. After the skunk walks away retrieve your cage. The blanket won't be of much use anymore.
I did that for my sister in law many years ago.