Honestly, I'd use the call-the-insulators-and-have-them-do-it method. I've had drywall mudders fill electrical boxes with joint compound, and I've had them remove it without damaging the wire, because otherwise, I'd have gone after them for the cost, including labor, of replacing any "unusable" materials.

Trust me, they didn't want the hassle of a lawsuit or to pay my rate for fixing the problem.

Now, if you really want to take care of this yourself, just strip what you need to, and replace any necessary insulation with "spaghetti", heatshrink tubing, or a combination of the two.

Larry
www.fineelectricco.com