I would sand it down with rough paper, then 400 grit to smooth it down. When free of all the original finish it will look like S**t. At that point use the 0000 steel wool or some 1000 or 1500 grit sand paper and smooth it down. Wipe everything with a lint free cloth. Then apply generous amount of Watco Danish oil which you can find at Home Depot( it comes in light, medium and dark walnut and other stains), giving it a bit of a wipe and let it dry overnight ( stand the stock/gun vertically).There will be a lot of absorption at this point as there is nothing blocking the pores.
The next day apply another coat of Watco Danish oil and 15 minutes later, wipe it off and let dry for a day. Repeat every few days for 4 or 5 applications.
I did it with a new Browning 625 ( because I inadvertently damaged the glossy oil finish leaving it partly flat and partly shiney.) I now have a super flat and rich oil finish.
I plan to apply a boiled linseed/turpentine combo 2:1, for a deeper finish, with a deep redish hint in the wood.(I have one gun done this way) It is rubbed in and applied with 400 grit paper so any pores of the wood absorb the minute bits of wood released by the sanding. The idea is to rub the mix(linseed/turp/sanded particles) with the palm of your hand until the linseed/turp gets warm and then some. At some point, after any application, when it is dry, run the 0000 steel wool over it - with the grain, to smooth any unsmooth areas. Weekly applications should result in a piece to be envied by onlookers. You'll have a shine, but it will look rich, not like a verathane gloss.
Only offered as a suggestion. There are many good ones that have been offered on this thread.
