It depends on what the firearm is, and how you define “cleaning.†In this particular case you want to remove as much crud and rust as you can WITHOUT REMOVING ANY ORIGINAL FINISH. The revolver is only of interest to a collector, and most collectors want as much original finish as possible including what they call “patina†and we would call tarnish. It is O.K. (in their view) to remove rust, but not any of the underlying metal. Anything that makes it look polished degrades the “antique†appearance. There is no objection in getting the rust out of the bore and chambers, and to do this I have CAREFULLY used rust removers such as Naval Jelly. Do not get any of it on the exterior parts of the gun, and following its use give the bore a good scrubbing to bring back as much shine as possible.
Others want to restore the piece as much as possible, as Josey does. While I have no objection to what he’s done, (and it wouldn’t matter if I did) he has in some cases lowered the price of what some collectors would give him. Frankly I don’t think he gives a hoot though.
I go both ways. If I should obtain a finish-worn and abused gun – particularly a post World War Two model I probably wouldn’t hesitate to restore and refinish it to as close to “as new†condition as I could. In any case I would return it to fully functional shape regardless of what I did to the finish. And I frequently use guns of this kind as a basis to build something customized along my own interests.
Resently I was ask to restore an old Colt revolver made around 1923. It had a little better then 95% of the original blue, and that blue cannot be duplicated because the technology that did it is no longer available. The owner suggested that it could be re-blued. I told him," no, doing that would cost money and reduce the value of the gun." What I did do was compleately clean it and retrofit some of the parts, generally along the lines that Josey suggested without doing any exterior polishing.
However, if I got something made during the 19th century that might possibly be unique (such as you have – I think that very few presentation guns like it were made, and probably fewer survived to this day – I would be very careful in restoring it beyond removing rust, and/or stopping further corrosion and taking steps to preserve any remaining finish. Hint: On antiques, especially plated ones, it is best to protect the exterior finish with a good wax rather then grease or oils.