Patina on antique furniture is one thing but English guns of quality were often returned to their makers to have their wear on finish renewed so there would never be any gun patina. Perhaps it might be different on a muzzle loader but doubles are expected to be kept in good repair with a nice looking finish protecting them for future use.

I would strip and refinish the original wood. I expect a little heat will remove the tip easily. From there refinishing can be a nice way to spend a few hours a night getting it exactly to your likening. And you are smart enough not to sand a stock to death. Done properly a good finish adds beauty and value to a nice gun.