If you know the thread diameter and pitch, it would be easy to make a shaft for it. You'd spend more than the cue is worth, but it wouldn't be that hard to do.
First, take it to a hardware store and see if you can find a nut that will thread down all the way on that screw. It could be standard or metric threads, so check them all. To me, it still looks like a 5/16-18, but it's most likely metric.
If that doesn't work, find someone with a good caliper and measure the diameter and the distance from one thread to another. It's more accurate to measure the distance between 10 threads, and divide by ten, or seven divided by seven, etc. With that information, you can probably figure out what thread it is, if it's a normal commercially used thread.
I hope that helps!
Royce Bunnell
www.obcues.com