If it's just dirty form grease and hand oil, you might try a soor satin polyurethane and your old stock looks me elbow grease, mineral spirits, and a piece of old T shirt.
often this will simple clean some grime.\I just posted a lament regarding conservation vs restoration, and you didn't mention if yours was a nice pre-64 or a post 64 shooter.
The next step would be Formby's or Minwax antique furniture refinisher and 0000 steel wool...mop-rub-remove with paper towl-repeat.
This stuff dissolves most finishes without the harsh effects of most strippers.
several in process n ow, and the method is about fails safe
Once it's cleaned to your satisfaction, 3 coats of rub on oil, or satin polyurethane, or tung oil and your ready for reassembly.
Tung oil gets too glossy for my taste pretty quickly, but it's a good finish.
Your old stock will still look old, but fit well, show the natural beauty of the wood grain, and retain the charactor and storied dents, befitting it's age and "experience".
DON'T OVER DO IT!