The first step in shaping a saw handle is to mark out the inner lines that you’ll shape up to.

Then it’s time to break out the rasp and file and wish you had a better rasp:

I didn’t use a center line along the edge of the handle this time. I just cut alternately from each side until they met in the center. I kept them even by measuring the depth with my double square. That tool should be dragged out back and shot for being so handy.
When it was all mostly said and done, except for final sanding, it looked like this (shown next to the old handle):

The next steps are to cut the holes for the screws and the slot/mortise for the blade. I am not looking forward to the slot. It’s where I can really screw up the whole thing in one simple, easy step.