I vote leave original. First, because the conventional wisdom these days with vintage is original all the way! But also for resale purposes. With the current trend for weathered or "Tropical" dials why not leave it in as found condition? And lastly, the purists, will raise heck after you change out the hands and relume it.
How about replacing the hands completely with nice ones that you like?
But keep the original hands during the term of your ownership & ensure that the originals are re-installed in the event of your disposing of the watch (or at least include them with the watch so the new owner can re-install them if so desired).
"It's only original once...." As the owner of many trench watches, I think that "preservation" is critical to the integrity of a 100-year old watch. I have had them repaired -- and the dial lightly cleaned -- but nothing to disturb its originality... Your watch is beautiful as is!
There are the purests... some of the seem to have spoken in the above posts. But if we left watches of this vintage in their "original" condition, they'd be still slowly corroding way. For example, the early non-breakable crystals made of cellulose, decompose over time and off-gas which in turn causes corrosion. Radium lume even when new only lasted (glowed) well for a limited time, before the bombardment of alpha-radiation onto the phosphor (zinc sulfate) caused the deterioration of the material. Thus, watches were often relumed as part of a service. The old material can be removed, and replaced with stable, non-radioactive material that is not continuing to deteriorate and possibly continue to cause deleterious effects on the mechanism of the watch. New material can be added with an aged look. But the ultimate decision is the owner of the watch... or current care-taker. ....and a good question to ask yourself: Are you wearing the watch or curating a museum piece?
Personally I have no problems replacing crystals and sometimes
hands if necessary or repair them. Anyone who has worked on a watch has done this.
I believe if the owner of the watch likes the hands re-done I personally do
not have a problem with it. It's a personal choice, it's his watch. If it was a rare or unusual
watch than most likely not. I have not studied the re sale of watches with re lumed watch hands
but if re sale is a goal in the future that would be something to think about
when re luming.
I know these are mostly not wristwatches, but they still represent different considerations.
This travel clock had lume applied to the numbers and hands (an available option) but the paint was in horrible condition, was flaking off and looked more like rust (right-hand image). I cleaned off the lume (left-hand image).
This pocketwatch had old lume that was flaking somewhat from the hands (inset image). I was nervous about the radium and cleaned the old lume out; the dial has nice stencil-cut numbers which hold the paint nicely (right-hand image). My restoration with modern lume is on the left. I did this about 18 years ago and might not have done it today.
This is another example that still retains the original lume (and radium-burn into the crystal). Notice the nice black outline that was part of the original numbers (also with stencil-cut dial). Too bad the modern lume in the hands does not match.
This World War I trenchwatch has original lume in rather rough condition, but because of the historic originality of this scarce watch I am not going to try to "improve" it. I regret somewhat that it will not be fully restored to wearable condition (movement and case are just fine), but as said by many - it is only original once.