Tinsel wire is easy to solder, just make an impromptu solder pot. A piece of scrap pine wood ( preferably with a knot that you can use) and drill a 10mm hole in it to 5mm depth, then simply make a pool of hot solder in it by feeding in solder and holding the soldering iron tip in it, then while still hot dip in the tinsel wire and it will tin. Pine knot works best, because the natural rosin in the knot acts as a very good flux, and keeps the solder ball clean and strips the wire coating off.
Just remember that you need strain relief in there as well, that solder join will be the weak point and will fail if it is flexed a lot, so ensure there is a firm grip on a non soldered bit of the cable to handle twisting motions and keep them away from the solder join.