Based on your measurement, #17 AWG wire is 1.15mm, pretty close to desired diameter. I would be super careful about soldering a solution as the aperture blade may warp with heat applied and become useless. Also, they are so thin that the metal may melt, opening the hole. If you solder, use a low wattage pencil iron designed for use with SMT (surface mount technology). Good luck!
Edit: I used to be a watchmaker years ago. The proper tool for doing the job is a watchmaker's staking set. If you can fab up a proper pin, find a watchmaker and have him stake it to the aperture blade.