Though I did this a couple of weeks ago, I haven’t had a chance to post it until now. I managed to acquire a small bench vise for metalworking, and bolted it to a board, which I then, in turn, clamp to the bench when needed.
This was necessary to cut the saw screw/nut hardware for the new saw handle:

I used a mini hacksaw to cut these “furniture joiners” down to size, and then a file to smooth them. Then I used a brace to bore the holes in the handle (holes not shown here, but I think you know what holes in a handle look like).
The handle is now in the finishing stage. I’m using a clear satin varnish. It’s almost done; I screwed up the last thick coat, so I’ll need to sand that level and apply one more, but I should have the end product ready next week.