One of my fav rifles is one of those in 30/06 and also have one in 270 I wouldn't recomend a refinish as they are light wood with a stain. I tried it on a 579 and just couldn't get the stain to take..my 06 had a really bad pad so I changed it out for a little thicker one to get som more length.
If your rifle is well used keep using it.. My 270 is in a McMillan stock and is a dream to shoot and hunt with but I still use the wood stocked 06 much more.