I have a call in to the local place I bought my king pins for my '36 and they're trying to figure out if they have the right cable or not as we speak... hopefully they do...
I guess the '37 and '38 speedos are quite different based on what you've said, tiny...
Mine has the typical screw on connector but it is what is in the center that makes it different... the '37 speedo has no hole... instead in it's place is a square piece that sticks out of the center of the gauge...
The cable goes over that, then the round screw on connector slides down and spins onto the back of the gauge to lock the cable in place...
I can try to take a pic a bit later if the shop doesn't have what I want... at that point I'll be scrambling to get something that will work... the count down to my first show has begun... I have 2 weeks to get the '37 finished, everything working, get it inspected and licensed...

~Trev