The books I've seen say that old stocks should be cleaned out with turps and a stiff brush. Most new stocks after they have been checkered are left untouched as the the oil would clog in the checkering making it look not as deep. I think if you use the above methods mentioned, you should be ok. Thinning it down sounds good and use a very small amount working it well in with your tooth brush. i would think one application would do as you don't want it to build up only to blend in with the surrounding walnut.
