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.
I created an account just to thank you for your answer. I just got a Stanley 45 and couldn’t figure out why my cam wouldn’t lock to the bar. I could see the threads didn’t go all the way through so figured there was something missing except that it’s not on the parts diagram I have.
Anyhow, your specs allowed me to remake the missing part.