Please note- double barrel shotguns frequently had the two barrels joined by soldering. Unfortunately, hot caustic blue will eat the solder out of the joint, and the barrel come apart.
The preferred method of bluing for these is rust bluing. Yes, you CAN do rust bluing at home. It will give a good blue, but is more of a matte, and not high gloss. Most cold blues will sort of, kinda, maybe do OK for a touchup- entire barrel- not so good.
My standard suggestion for light surface rust- go to the gocery, and get a CHORE BOY COPPER pot scrubber. Be sure it is not copper plated steel, but copper. Wet it with a light oil (I like Kroil, but use what you have) Rub lightly, change to clean area on the pad periodically. Gun will start to take on a coppery hue- wet it with clean oil, rub with clean soft cloth- it comes off.
Copper is softer than the steel of the barrel, and will not hurt existing blue. Steel wool CAN if you overdo it.
