I have no screws to remove or measure. Pic is from google. Need the size and pitch to find suitable replacements.
You got threaded holes to work from?
I have used tapered splinters of wood, or softer metal than the part, to take impressions of the threads from a hole. Can be a bit fiddly, but with care, you can get a really close fit, and then measure the thread against a pitch gage and measure the diameter. Use a magnifier!
From there, compare to the standard sizes to see what is closest, that might work, and if that does not get you a match, you end up making a test thread on a lathe, seeing if the fit is satisfactory, and making adjustments on the next one, until you get a good fit.
Per above, you could always adapt it to a close to original known thread size. Aside from the UNF, take a look at the UNEF (Unified National Extra Fine) as well as UNS (Unified National Special, which can cover pretty much any odd combo of pitch and diameter, as long as the basic thread form stays correct).
I know there are some collectors out there specializing in Winchester sights, I would think they would be better reached through a more focused Forum.
Any used Gun Parts dealers out your end of the country? They usually travel to any reasonably close gun shows, and are a large part of why I went to as many gun shows as I did.
It may be worth sending an information request in to the Buffalo Bill Museum, in Cody Wyoming, with an information request. They hold a large collection of Winchester Factory engineering drawings, and you will never get a better source than a factory drawing, if they have it cataloged somewhere in their archive.