I have had cats for years and never had this problem. But if I did, I think I'd just spray vegetable oil on the trunk. Seems like a solution, but I just made it up, so might be solid fail too.
I'd do anything to see my cat playing in the tree again. We couldn't really stop him. He loved Christmas we loved that he loved Christmas. He never hurt anything I don't think but I think he may have zapped himself once. He would hang out under the tree mostly, we would always put the soft unbreakable ornaments at the bottom of the tree we called them cat ornaments he would bat and play with some of them. I miss it.
The first year we had our cats they loved to climb the tree. First time we saw it I told the wife there must be some mice in the tree. She was a bit upset about it, but I got a good laugh.
Next year the cats couldn't care less about the tree. I'm guessing it was because they could go outside and play in all the trees they wanted.
Cats will do what they want to do when you aren't looking. We just fastened the tree to the ceiling, old house, to keep the tree upright the first year we had a climber. Following years no climbing. The tree skirt was a napping place and the water reservoir was for a flavored water drink.