To Refinish or not to refinish, that is the question.
Urban,
Your gun, your property, you can of course do what you wish.
But if an antique, why refinish? If there is any or even no finish left on the gun, refinising will reduce its value by at least 50%. If this is a $50 item, then big deal.
A pistol that is over a hundred years old and looks it in my opinion is fine, that is part of the character of an antique. I have several. Some I refinished. Some I just cleaned.
Unless the pistol has some major rust or flaw, my choice would be to leave well alone. I kinda like the feel of the metal with honest wear. Gets my imagination going, the stories the pistol could tell if it could talk.
My favourite pistol has less than no finish on it, it is all brown patina and has a finish similar to an old set of mechanics vice girips. But it is antique and to me it simply looks right. It shows several lifetimes of use and abuse. It functions flawlessly, that is what counts.
I do the resoration myself. I tackle blueing in my garage. Since the finish of these period pistols is often oil blackened, that is the process that I use. With careful preparation, I can put back what looks like an original finish.
To get it re nickle plated, you can find platers in the yellow pages, but you really would need the services of a gunsmith to get it done. It has to be dismantled, plated and reassembled. Not some thing that Toni at the local plating shop might be able to do.
Make sure that you are sitting down when they quote you the price, might as well get ivory or mother of pearl grips made while your at it!
Old beat up and peeling nickle is best removed with electrolosis as opposed to polishing, and then the gun could be blued.
For example this little pistol I did was rusted solid when I got it. I let it sit soaking in a jar of diesel fuel for a few weeks to free it up. Too far gone to clean up. Er um

, finger prints aside, the scanner pic shows colours on the frame, but to the eye is actualy very dense black, the light refracting comes off with purples and blues. Same classic period finish as original. I even polished in two directions to try to duplicate Webley's process.
These were made in the days of hand tools and basic machinery. I fabricated some replacement parts with handsaw and files at my bench and modified some springs from another pistol to get it functional.
The bore is 'dark and frosted' as they say. The outside looks nice though. It is one that people reach for when looking at my collection.
The cost of refinishing? Approx $5 cos I had to buy extra fine emery paper and fuel for my coleman stove.
In this case I might have brought its value up from my original $25 purchase price. I have however, ruined the collector value. The thing now looks mint. Doesn't look antique any more. Maybe I will buff the sharp edges with steel wool to give it fake age wear.
Another pistol saved for future generations. My work here is done. 'Hi ho Silver, away!'