Nikon FM Film Fork
Why dont you try grabbing a flat head screw driver, wrap the tip so it doesnt scratch the inside paint, put it between the prongs and unscrew the whole rewind. Then replace it in reverse and try to screw it all completely in tightly holding the screw driver in place. You dont want it to be loose or when you try to rewind film it may just unscrew over time. Hopefully that will work.
Edit: sorry dont know how i skipped passed what you typed about the screw difference. The end of what i wrote applies still. A tight rewind assembly is important. You can try to find a similar size screw from another parts camera to replace it, or maybe from an eyeglass repair kit.