I would have personally left all that grease... It would have waterproofed the wood and been better for the gun... I would have applied two coats of a product called Atsko Sno Seal to the Stock and buffed with a clean non linty rag (preferably a new bath cloth) The product is made of beeswax and silicon and will waterproof leather and wood. Good for both. It will slightly darken the wood though, and from the sounds of it, you want the wood brighter and cleaner..
Looking good so far, I advise over applying that Oil for finish...
Clean the gun barrel, tube, and action well.
HERE IS THE BEST ADVISE I HAVE TO GIVE YOU...
For lubrication on bolt actions (especially heavy bolt actions) ; Use ten point crossbow rail lube 3 parts, 5 parts heavy gun bolt lube (These are the small containers of dark heavy grease that where issued to M1 Garands in WWII that you find laying around at gun stores for 25-50 cents a piece - this stuff is wonderful when mixed like this with lube and petroleum weathergaurd), and 2 parts Hoppes Weathergaurd gun oil. Mix these together with a stirrer in a container that works for you. This grease will work great.
I also use and suggest tenpoint crossbow rail lube for all 1911s (for contact points between frame and slide) These areas are very high friction in 1911s..
As a matter of fact, the frame/slide friction is why the original 1911 Gov't A1's could not be reliably automatic. Original Auto 1911's would have failures here.... Apply 2 pin head sized beads on the front of the frame 1/2 inch from the lug nut.. And two pin head sized beads of this lube on the back of the frame where the checkering/contouring is... Perfect frame/slide contact lube for all 1911s...
Anyways, This mix of oil/lube provides the perfect amount of lubrication for optimum performance of the bolt action on both sporting bolt actions and is perfect for military heavy bolt actions (such as mausers with heavy actions)...
As a all purpose gun oil I suggest using a product called ballistol. It is german made, and you will probably have to order it. However - it will not darken wood, and is actually good for wood as well as metal. This is the best gun oil that you can buy for your wood stock rifles and wood handled pistols.
Hope this helps you.
All the best.