In general, leave it alone. Write up as much as you know about the PO and the story, date and sign it and put the sheet of paper in the butt trap.

A very fine stainless steel brush with oil and gentle use will get most of the staining off if concerns you. For the love of Pete, do not sand, steel wool or strip the stock, just oil it.

If you think the metal is dry under the wood, you could take it down and address that if necessary, but resist the temptation to clean off all the patina and residues.

For a time there was a mania for "refinishing" vintage and antique furniture, then gradually the light went on and people realized the value of patina. All the pieces they ruined are worth far less today.

The day will come when "unrestored" surplus rifles will be worth a premium because that status will be the best or only guarantee of a rifle's originality.