If you can remove the old finish without a complete strip, you will probably retain the original color. Several years back I bought several stocks that came from a facility that was de-miling M1 Rifles. If I remember correctly the tags were from AMF, and had the original rifles serial number. Some were absolutely coated in old finish, which I stripped with lacquer thinner. The lacquer thinner removed the old coats, but left the nice red color, and a few coats of the BLO/Turpentine restored them. All the stocks I bought still had the original cartouches, and getting the old coats of what was probably raw linseed oil applied by recruits enhanced the cartouches.
Raw linseed oil will never dry completely on your stock. Boiled linseed is better. I prefer real tung oil. Most "tung" finishes are heavily modified polymers. Behlen makes a true tung oil. Several coats sparingly applied, followed by a mix of 1/3 tung oil, 1/3 turpentine, 1/3 beeswax melted together over a low heat. Work the last coat with your fingers, then wipe with a clean cotton cloth. Regards, Clark