As you have likely discovered,,, the paper outer portion is attached to a plain brown cardboard box. I used a fiber reinforced shipping tape to my corners,, allowed them to dry, and was able to get it under the outer paper. It's a tedious job when the box is well worn & broken,,, but once completed, can & will look better if done right.
I've never added any exterior stuff like you mentioned over any of my older boxes that needed any repairs. I chose to allow the box to look as original as possible, yet, I put a note with each box stating it was "restored" if work was done on it. That way, in the future,,, if I'm not around,,, my estate can give a proper description of them to any potential buyers.