If you like the looks and color of your existing finish you won't have to remove it.
You should wipe the surfaces with some ammonia to remove any waxes that may have been applied and a washing with some soap and water to remove any trace of he ammonia would follow.
If your stock has open grain (little pits) like most Walnut stocks do you will have to fill these pores with a filler. Birchwood Casey makes a filler called "Gunstock Sealer & Filler".
You apply this fairly thick and rub it into the pores and let it dry for awhile. Then, using a course cloth rub off the excess rubbing accross the grain,
not with it in the direction of the butt/muzzle.
If a few of the pores don't totally fill, the oil you apply will fill them but if there are some pores that are totally empty, the oil probably won't totally fill them. These little pits will be very obvious after the stock has a glossy finish so do a good job of filling them.
Get some Tru-Oil, a Birchwood Casey product that is basically a linseed oil with dryers added.
Because it is a simple oil it won't dissolve your existing finish.
Apply the Tru-Oil with a fairly wet coat and allow it to dry at least 8 hours. Then, repeat the application and allow it to dry.
While its drying go to your hardware store and buy some 600 or finer grit wet/dry, black sandpaper. One sheet will be enough.
After the second coat is dry, tear off a small piece of the sandpaper and wet it with water.
Very LIGHTLY sand the surface to remove any of the little bumps that dust causes. When the surface looks uniformaly dull (the paper will not polish the surface, it will scratch it), repeat the two oilings and sandings as you did before.
Do not try to remove anything except the little bumps.
If these little bumps or some 'orange peel' finish is left on the stock they will stand out like a bad case of zits at the High School Ball.
After at least 6 coats of finish have been applied, do not sand the surface. Just allow it to dry.
Buy some "Wright's Silver Cream" and using a piece of soft cotton material apply the creme and rub the surface using a circular pattern.
When the small area looks polished, move on to the next area.
This is a labor intensive job so be prepared for a lot of rubbing. Do not try using a courser or more abrasive polish or you will dull up the appearance.
When you have finished your stock should look like Walnut versions of these.
By the way, I had to work at making these not 'mirror bright' after doing what I've described above.
If you just stop with the silver polish the finish will look like a high cost Browning or Weatherby.