Do you intend to remove the old skin?
First, why did the original door get damaged? Sun? Water? Lack of constant maintenance?
I am assuming it is the outside surface?
Any "skin" would need to be done with exterior rated glue of which I doubt and 1/8 veneer ply is. You could probably get away with it, using powered resin glue. Finish is critical. Edge will remain venerable.
ou need to pay attention to the thickness and how it mates to the weather-stripping. If peeling paper thin veneer and adding 1/8 ply, then you have a big weather-strip issue.
I have seen come creativity using Formica, but only in a mid-century modern where you can have fun.
Often it is the bottom foot that is beat up. Common practice is a brass or stainless "kick plate" to protect the bottom of the door. ( and cover up damage)
Personally, it makes more sense to just get an insulated steel or fiberglass door unless you really want a natural wood finish. If just a slab door, then probably again best to get a new slab and get creative in protection.
This is an eight year old wooden door, that has been stored all this time. Unfortunately a small leak in building got to one side of double door. No rot. I already decided to use a skin of metal on bottom portion about two feet. I thought with a little luck I could remove skin, prepare and resurface with another skin before adding metal part. Will be an outside door. This is one of those determined to use rather than buy another door deals. Plus short of money.
As others have noted the doors do not hold up as they are not meant for this purpose. I had a temp door like this I used for 6 months on a project before I got the final door built. It soaked up water like a sponge. Despite being painted and the top and bottom sealed with silicone.This is just a small storage building the doors are going on.