Just clean it. Winchester had an oil finish,,,,dont use any of that shiny crap on it. It should only turn out as shiny as the amount of rubbing effort that you put into the oil.
Any refinishing that you do, other than cleaning it likely decreases its value, unless you send it to Turnbull, and then restoration costs begin at $3000 and up. Depending on the condition of the stock and if someone has varnished it or not, I would use a solvent like paint thinner and nothing more abrasive than 0000 ~~4 OUGHT~~ STEEL WOOL and gently go over the finish and remove old surface grime, use a toothbrush to get around the metal pieces then let it dry and re-oil it with linseed or tung oil depending on the condition of the stock. A new 97 in 1907 would not have had a shiny stock. My Great Grandfathers 97 has an oiled stock.
Whittington Center Life
Times are tough, ammo is expensive, there will be no warning shots.