So I don't have any old axles around; West Marine doesn't have a 10mmx1.0 bolt; I didn't get to Fastenal before they closed for the weekend...however, I searched Home Depot online and found a store in the area that does have an M10x1.0mm bolt - 20mm long! I'll be there tomorrow.
Next question: 20 mm will be too long so I'll have to cut it down. I know from previous experience that cutting with a hack saw mangles the threads at the end. How do I clean up the threads so they will engage well with the eyelet on the frame?
One approach that occurred to me is to cut the bolt while it's screwed into the frame. Then maybe when I back it out, after cutting it to length, the threads in the frame will force any damaged threads on the bolt to the correct shape. This assumes that the steel of the frame is stronger than the steel of the bolt ( I have no idea if this is the case). Otherwise, the damaged threads on the bolt will only ruin the threads in the frame, which, obviously, I don't want. Is there a better way?