Most cold blue is a flash plating of copper and selenium dioxide. The old test to determine if a gun has been touched up with cold blue is to apply Flitz or Simichrome polish to a small pad, and rub it. These polishing compounds will remove the loosely bound cold blue, and leave the original remaining blue underneath intact. But naturally, being very fine abrasives, with enough rubbing, they will thin or remove original bluing as well. Of course, fine sandpaper, emery cloth, or Scotchbrite pads will be more aggressive and much more likely to cut through to bare metal.
Many brick cleaners contain hydrochloric acid. Using hydrochloric acid (or muriatic acid), or things like Naval Jelly (phosphoric acid) would likely remove it as well. But they will also remove any remaining original blue or brown, and leave you with bare metal, and no Damascus contrast. This may be fine if you plan to refinish the barrels with rust bluing and ferric chloride etch to restore the Damascus finish. They can also etch or frost the surface, and really need to be neutralized, as Mike said.
