I have replaced both the entire innner and outer roof panels on my '57. The cab is the same as '59. Are you just trying to replace the inner portion along the windshield? If you are, that means the outer roof panel is still in place, this is good. This means that there is still structure holding the cab somewhat square.

That panel above the windshield is spot welded along the length of the windshield to the outer roof panel. You will need a good spot weld cutter with a couple replacement bits. You will also need a bunch of vice-grip type pliers. Just get a bunch of the cheap ones from harbor frieght. The ends of the panel are tucked behind the a-pillers and spot welded in a handful of spots and may be brazed as well, cannot remember off the top of my head. I agree with Bartamos in that only replace what you need. But with that said you may open it up and find another can of worms. I would weld a piece of square tubing across the windshield opening, and maybe two others crossed "x" from corner to corner to help with bracing. I also welded two braces straight up from the floor to the bottom of the inner windshield opening. This was so that I could ensure the windshield opening stayed the same, you can see in the pictures below.

Here are a few pics of when I did mine. Might give you an idea what what you could be getting in to. https://photos.app.goo.gl/T86g0LLLPL5nZyJs2

All in all when I did them, i was super nervous cutting into that much cab structure, but it went MUCH smother than I anticipated. Still had to do a ton of beating on the panels to get them together correctly but it worked out.