If you have an old glass flower vase(clear glass, tall and wide) put the head of the stock face down in the vase and fill with acetone. In short order you will see the acetone discolor if there is oil left. If you are concerned about the pad fit, then experiment with using the steam around the pad first, it might lighten it enough and you can pass on soaking the butt area. But if it were me, I would still soak the neck and head in the acetone cause I'd want to remove as much of the oil as possible.
Good luck, carl
