The most amazing thing I have learned about cleaning gun finishes is a product called Scrub Budz .
I am not certain about that spelling, you can look it up on eBay and get it right. It is an Amway branded product.
As to what it is, I amsure you have seen & heard about Chore Boy scrubbing pads which are made out of copper.
Scrub Budz are the same sort of stuff but made of stainless steel. They are much coarser than any steel wool you are accustomed to I'm certain.
Now the majic part. These scrubber pads must ONLY be used dry on a blued firearm, and when used as described there will be absolutely no damage to the blueing on the firearm. Positively amazing.
Now how it will work for the OP's problem of rusty fingerprinting on a gun with barely any finish, I don't know.
I have also found that the RB17 product is a superb rust removing product that when used with an appropriate abrasive media, removes even scaly rust deposits without affecting the surrounding areas.
I also like the rubberised abrasive scrubbing blocks available in several differing grades of abrasive. Again, these must be used dry, but can remove oxidation from many types of metals without abrading the base metal to any appreciable degree.