cutting the thread with a die would lead to quite big cutting forces. I'm not sure that the barrel really is intended to withstand them. On the other hand side sigle point cutting on the lathe is a very fine process when done in several cuts (and always stopped before the shoulder). For this small amount of thread it would be sufficient to use a metric lathe and choose a pitch that is close.
Typical dies also need some turns to cut to full depth so the last threads to the shoulder might no fit into every nosepiece.
I'm not anticipating any undue cutting forces. The thread is very fine, so intrinsically requiring less force, going onto brass and there will be only about 4 of them; not requiring anywhere near the force encountered by most of the other threads I've cut in the past. This is also a fairly beefy, one piece barrel : not one of those thin walled cores with the external cosmetic sleeve and I probably can grip the flange, when turning the thread. Quality dies can also be adjusted for depth, finishing the thread in more than one cut.
Whitworth threads are difficult to cut on a lathe. I know that people make do with metric lathes but the crest and root have a rounded form. This posed so much of a problem that the ASME developed an alternative truncated thread in 1958, that allowed the use of conventional machinery to make microscope threads. The truncated thread ANSI B1-11 1958 (1972) presumably became adopted . I haven't looked at any of my American made stuff closely enough to see if the crests are flat. The truncated thread crests pose zero problem in this application, it's not like they are being used to mount rocket launchers, so I probably could get someone to use that form, since I have the specification. I do have access to a shop that cuts Whitworth threads for aircraft parts, so I could go there but the objective isn't important enough to me, to spend 50.00 or more to thread it. It just has the correct specs. on the barrel, so I would like to use that barrel. If I can't get a thread on it easily, I will just swap the optics over to a plain barrel, which would render it fully functional. The two barrels are identical; just one has bright phase, stamped on it.