Two ways to go to clean. One, only if you are prepared to stain the stock because it will need it; take a piece of folded terry cloth and some lacquer thinner and basically wash the stock with it, maybe using a toothbrush here and there. It evaporates quickly and there is no chance of swelling any wood. Two, wipe it down with Turpentine on a folded terry cloth. This will remove dirt, oils, etc. but not the stain to any great extent. I do not ever use any water or soap on a piece of wood except water for steaming dents.
Once the stock looks clean, and after staining if required, then you can take raw linseed oilcut with Turpentine 1:1, put it on a folded terry cloth and begin to oil the stock.
I was fortunate once many years ago when I was corresponding with a carbine specialist in another state and he mentioned having several gallons of arsenal stock stain from Rock Island. I talked him into selling me a pint and that has been incredible. In the can it looks deep blackish red/brown and smells like Turpentine. You put it on a folded cheesecloth and wipe it on like any stain of that type but the wood has to be stripped for it to work. I discovered what lacquer thinner does just looking for a quick way to strip one.
The thing is, you don't want to strip a rare of valuable stock except as a last resort - that's why you use just Turpentine if its a simple cleaning job.
I