Agreed, a picture is worth a thousand words in this case. But, I'll take a stab at it.
Do they look similar to these?
If they are then know that they are ultra delicate (oh, you already do).
Do you know what material the insulation is made of? Is it a coating such as lacquer or a jacket of made some plastic?
If it's a jacket then just stripping the ribbon back may be difficult depending how tough the material is and using a razor knife will be really hard to cut just the jacket without scoring the ribbon. Any scores or cuts in the ribbon create a new weak spot and a possible increase in resistance.
If it's a lacquer similar to magnet wire then sanding will be the only way to do it and again you must use care and go slow. I suggest you start with some 220 grit and see how it does. Hardly touching it? Drop down to 100-120 grit but I would not use anything coarser. Just get the bulk of the coating off and then switch to a finer grit and maybe even a wet/dry sandpaper. Once the metal is clean then you can solder them back together if there is enough material there. Oh, and it will affect resale value.
