Re: .300 rum
To my knowledge, yes--any long action stock will do. But I'm confused as to the second half of your question. Are you asking about just re-boring your existing barrel? If so, then no, that's not all you need to do. You need to make sure you have a magnum bolt face, and you'd be better off just buying a new barrel. This post would be better suited in the gunsmithing section, I think.
God Bless and Shoot Straight