My approach is different. I think the cats would make THE BEST CHRISTMAS TREE DECORATIONS ever. Don't use glass balls and use twist ties to attach the ornaments to the tree. Firmly anchor the tree so it won't fall over just plan for the cats to be in the tree to begin with and it will reduce your stress level tremendously.
Our one and only house cat loved to perch in the tree and swat at the dogs as they went by..... for our family the joy of seeing our animals enjoy the season and the special "treats" they brought were more important to us than having a "department store" pretty tree. Granted by the time Christmas came and went we could have won the prize for the WORST DECORATED TREE..... lol... those were the good ole happy days.
You brought back memories of the days when Boo the Boxer was a pup and would promptly unwrap every single present put under the tree. That year we laughed more and wrapped more and Boo was ever so much fun. She never damaged any of the gifts, just took the wrapping paper off.....