5717s is basically phosphoric acid, and as an auto painter, I used it to remove rust on bare metal before priming and painting. It worked extremely well, and the reason I'd use it was to stop rust from coming back under the primer coat--you see that all the time--bubbling paint jobs with rust underneath. Dupont, PGP (Ditzler), BASF, Sherwin-Wms, et. al., all the big paint manufacturers have their own product, and they're all pretty much the same.
If your problem really is
just surface rust, maybe a rough terry cloth towel and a lot of elbow grease will be enough of an abrasive to use with 5717s. I never had to worry about scratching the metal, so I always used 3M Scotchbrite pads or in extreme cases, a wire brush. (if your shotgun is SS, though, I don't see why Scotchbrite swirls would be cosmetically detrimental.
The stuff's expensive; see if you can find an auto body shop that will sell you a pint or less... I'll bet it'll be hard to find here though. Most shops will skimp on the expense and go straight from grind to prime.
It's been years since I painted... I can't remember which OEM brand I used that used to darken the metal surface while it etched the metal. I'd suggest calling DuPont before you commit and see if a tech there can tell you if their product just
removes rust without changing its' color.
As I said, every paint OEM makes a variation of this 'metal prep' product; calling around to the different 800 numbers will find one that doesn't "stain" SS while it cleans.