Those are Jim Badger grips. Jim was the previous owner (original) of Badger grips. I have picked up a few and they are very well made and fit superbly. The screw looks original and I have found one or two sets that had a brass spacer to prevent overtightening. They look to be original shape though they vary. How about a pic of the inside? He used a couple different blind nuts that look like a brass washer. Here are a few others.
Agreed you should. I prefer the looks of a slotted fillister screw and you can replace the hexhead one with a stainless or blue 6X32. Make sure to keep the original though.