Hi Jerry, my story might give some Quietcomfort, but not much else.
I had the original Bose wired noise cancelling headphones from 1997.
After about 15 years and ~ million miles of travel, one of the fine braids broke off at a pcb pad.
I recall having a difficult time heating with iron, fluxing and scraping with scalpel until I suppose about 3/4 of wires were tinned and some were broken off by the scraping.
After about 2 more years, the cable broke inside the jacket at the entry to earcup , so I called it unrepairable.
For homebrew transformers magnet wire ( 18 to 30 g), I use a small oxidising oxy-acet flame, and quickly pass the end through. After scraping the soot off, the copper is very clean.
But this method would surely melt those fine braids.