The finish is standard gun blue applied over a bead blasted surface.
Steel wool and other abrasives will damage the finish.
Get a can of Kroil, although CLP Breakfree will do.
Liberally apply it to the rusty areas and let stand for a day or two.
After soaking for a few days, apply more, then give the rusty areas a scrubbing with a brass "toothbrush".
This will loosen the rust without removing the bluing.
Wipe off the dirty lube, then spray the entire gun, inside and out, dripping wet with CLP Breakfree in the aerosol can.
Let stand 20 minutes to "soak" into the rough blued finish, then wipe off the excess.
This will build up a layer of Teflon in the rough finish and will protect it from further rust, and will continue to loosen and remove any remaining rust.
When using CLP Breakfree, SHAKE THE DICKENS out of the can. It settles and needs to be well mixed.