Congratulations on the find. Sorry I took so long to answer but here goes. I measured the parts but have to guess on the threads-per-inch since I don’t have a thread gauge. The screw thread could be a 1/4 inch outside diameter, 28 or a 32 TPI and I would recommend going to a specialty fastener dealer and trying them since Stanley is widely known for using unusual thread configurations. First there is a brass pin (post?) that goes in the hole that applies the pressure to the arm when the screw is tightened. Mine measured o.507 in. long and 0.205 in. diameter. It allows clamping without the screw turning against the arm. The screw itself was 0.508 long overall with the head measuring 0.375 in. diameter and 0.152 in. thick, reducing down to 0.250 outside diameter for the remainder of the length.
Hope this helps and have fun.