Yep you can rub vigorously with the stainless wool wont hurt the finish of the metal parts but do not use it on the butt plate or brass butt plate or they will be damaged.
Also not just any Turpentine or its derivatives its got to be Mineral Turpentine not Pure Gum Turpentine or anything else. Your good to go but also read up how to strip the rifle down there is scads of info on this site it only has to be down to its major components its only a tidy it up and get the wood looking not so dry.