Well, it's pre-1960 but not nearly as old as 1930s.

Old Dude, I really appreciate your comments, if only for general information value re guitars.
I'm not especially concerned with resale value, though, for reasons I gave above. I was more worried that if I tried to substitute a 'generic' screw for a specialized one, it might affect the longevity of the repair or otherwise interfere with the guitar's excellent ability to stay in tune.

I'll probably head over to a geetar shop today, with the guitar, and have their repair person find me the suitable screw.