The coating on the Summit cables is just heat shrink tubing. The same stuff they use on electrical cables.

Getting it off would entail using something like a razor blade to slice the tubing and peeling it back until it is fully off. There should be no adhesive involved.

Take the new heat shrink tubing and slide it over the length of the cable, and hit it with a heat gun. As an alternative, you can use a propane torch, however you need to ensure you don't get the tubing too hot that it burns.

The tubing is available from just about any electrical supply house.
Digikey (www.digikey.com) carries the tubing in 4' sections for $2.71 each (part #:A034B-4-ND)