The steel on the frame will retain its hardening after the colors have been removed. You might try a thorough cleaning on the frame before you try to remove the colors, so that the patina remains but the crud is gone. If you decide to remove the colors with the wood on the gun, tape off the wood and polish the frame with Flitz or Simichrome. Some have reportedly gotten a nice French Grey finish by using EasyOff Oven Cleaner on the frame, but this would require disassembling the gun. It may look nice, but it won't look right on a boxlock Uggie. Regarding the barrels and considering the value of the gun, you might consider refreshing the bluing with Oxpho Blue, available from Brownell's.
