How would I line a real fox fur purse?

About 4 years ago I bought a purse made of scrap fox fur that was left over from a project the artisan was doing. It's a beautiful purse and the fur feels very high quality. However the purse is unlined, it's just the tanned fox pelt sewn into a soft, unstructured purse. I would like to add a satin or other sort of lining to the purse because in these four years I've never worn it for fear of damaging the pelt with things like keys. It's just been a wall decoration. I've never worked with fur before, nor am I good at sewing, and I'm afraid of ruining the pelt by trying to do this myself.

Is there a simple way to line a purse like this that I'm overlooking? Or, if this needs to be done by someone with more experience, where would I go for that? I don't have any contract information for the person I bought it from and I am not aware of anyone that works with fur in my area and could help me with this. I live in the Willamette Valley in Oregon if it helps.