The copper-cotton wire is called Tinsel and the way I was taught to solder it during Air Comms Trade Training years ago was to take some finer single-strand tinned copper wire and gently wind it around the exposed conductor-cotton in a whipping fashion. Apply a tinned soldering iron to the whipping, wait until the insulating laquer 'burnt off' and apply fresh solder containing flux, covering the whipping. Remove from heat and cool. Cut off any whipping loose ends et voilą!