Loggah, I just measured two examples, both are 0.784" measured on the unthreaded shaft, that is smaller than a #2 screw which is supposed to be 0.0850"max/0.0822min - so a #2 screw will not fit without distorting the threads. I tried a #2 screw and it will not fit in the unthread clearance hole. The screws are probably an obsolete fractional size, 5/64" is 0.0781. The thread appears to be 80 TPI.
I ran into this size screw diameter on some sights I was making parts for but the threads were 56 TPI. I screwed one of the 0.0784 x 56 TPI's I made into the sight post and it was tight but it went since the threads are deeper and there are very few engaging. The original screw still fits, so it did not seem to damage the threads in the sight post.
I would try a metric m2 x .4 x 4mm long which would be close @ 0.784 x 64.5 TPI, still not the correct threads but they would be deeper cut, It would be just a little to long, 3.5mm long would be closer but does not seem to be a length that's offered and the correct head shape would not be available.
I used a special thread metric m2x.45 tap & die for the sight screws & nuts I made , that converts to 0.0784 x 56.444 and I needed 0.0781 x 56. The nuts fit the original screw in one of the sights and I used the metric die to make the threaded shaft for the other sight. I turned down 3/32" (0.093") welding wire to a rough 0.078". I also had to make the windage slider and an eye piece.