Go carefully there. Kynar tends to wilt at soldering heat. Press insulated wires together when they're still hot and suddenly they can be kissing; a 1-diameter short is easy to overlook when you're inspecting your work.
I find it worthwhile to use teflon-insulated wire here. When I'm building a prototype, the last thing I want to have to distrust is my construction.
True. Kynar is good for toughness around square-cornered wire wrapping posts. Teflon will survive a touch of a soldering iron.
I found my wire-wrapping gun recently. If I put in new C batteries it might work.