To get the grease/oil out of old military wood (or any wood for that matter), I acquired a 8 inch dia. PVC pipe, 5 feet long. I bought a cap and glued it on one end, and a screw cap on the other. The opening is still eight inches. To degrease, I remove the wood from the gun, place it in the tube, fill the tube with dry cleaning fluid (or varasoil) and let it soak for several days. Remove the wood, dry it as much as possible, then set it up and let it air dry for several days. Most of the time one soaking will get all of the oil out of the stock. If necessary, repeate the process. This also works great for the action to remove all the crud that has accumulated over the years as well as the cosmo and grease from depot storage.
The smell from the dry cleaning fluid will disapate after a few days, and you will not be able to detect it.