Eezox is to my mind one of the finest cleaners and best rust inhibitors on the market. Clean and oil your gun with Eezox. Wipe off all but a thin coat and let it dry. In my experience there will be no migration and your gun will be well protected.
Eesox is a wonderful gun lubricant/protectant. I wish someone local carried it. Bought a can at a shoot out of state once and it is finally gone. I would spray guns down after a rainy day shoot wipe off excess, and consider it done. Also neat smelling wife always could tell when I used it, and said it smelled great. used as directed it don't migrate and it is great for all forms of autos, rifles , pistols etc.