Hey Dave, that looks to be about a 3/8" diameter stub. I think you might be able to leave it as it is and drill and tap a 10-24 thread into the center of it and then screw some threaded rod into it. Then put a threaded insert in the handle and screw it right into it. If there is a piece of the 3/8" thread in there, you could drill and tap into it and screw it on the threaded rod.
Cheers, Jim ........................ Variety is the spice of life...............Learn something new every day