That is a tricky one John. I suppose a lot depends on the condition of the gun. Sometimes as I quite like to see old repairs and bodges on guns, but I am not a collector, just a big kid and I enjoy plinking. If the gun were really cheap and not in great condition, I would happily plink with it with the cut down barrel. If I was more into collecting and could do the repair so you couldnt tell, then I gues that is what I would do.
Think about some of the repairs / updates and refurbs that Webley have done over the years. Maybe the extended barrels replaced with shorter ones, gun reblued (The Juniors because of the frames going the colour that we now like). If they were done at the factory within a certain period I'd guess they were still "period".
I've been told that will some of the longer Webley pistol barrels, that there was not a set length for them , so one might be 1/4 inch or so longer than another of a very similar age.
If the inside of the barrel of your pistol was badly corroded and it wouldnt shoot well at all, I think that would be a good reaason to fit the other barrel if you wanted to use the gun.
At the end of it, it is your choice. If you accept you may knock something off the value of the gun but you will have the enjoyment of being able to use it, I guess you have to decide what is worth it to you.