This link gives a great resource for wire specifications, including dimensions (with and without various builds of insulation):
According to this resource, 22-1/2 AWG would be closest to 0.60mm.? Good luck finding that in small quantities!? Either 22 or 23 would work, however, 22 would be more common.
Wire size is measured by the size of the conductor, not the insulation.? Various insulation types are defined in NEMA MW-1000 standard.? The insulation layers of the various types of insulation can be single, double or triple build.? There are other specialty wires that have thicker and other specialized insulation types as well.? Insulations are rated by temperature and resistance to various chemicals and environments.? MW 35-C while rated to 200 degrees C is a good insulation, however, it is difficult to "burn" off the insulation and must usually be abraded or scraped away unless other caustic methods are used.? More commonly (typical of amateur radio kits) MW 80-C spec'd insulation, rated to 155 degrees C, is easily burned off with solder temperatures.
72/73,
Mark, NK8Q