Yes, we implore you, don't refinish the gun. You'll destroy the historical value. If you want the wood to look brand new, I'd suggest buying a new made stock set and saving the original. Might I suggest giving the wood a thorough cleaning first? You'd be surprised how great these can look.
Lots of methods out there for cleaning. A decent one with an easy to follow tutorial can be found at Midway USA(gunsmith supplier web site). Go to the learning center and they have a bunch of videos that are really great. I think the one you're looking for is about cleaning up an old rolling block. Good luck and post some pics.