On Tue, 7 Aug 2018 09:24:55 -0700 (PDT), Peter Easthope
wrote:

I aim to break off the entire crumbling jacket before enclosing the
wires in the heat shrink. At the ends, two layers of shrink might
be necessary to fill the strain relief. For durability, two layers
can be applied on the entire cord but that will make it stiffer.

You can easily get rather flexible polyolefin shrink tubing:
https://www.google.com/search?q=polyolefin+heat+shrink+tubing
https://www.delcity.net/store/Viton-Flexible-Shrink-Tubing/p_818844.h_818845
https://www.3m.com/3M/en_US/company-us/all-3m-products/~/3M-Very-Flexible-Polyolefin-Tubing-VFP-876/?N=5002385+3294230636&rt=rud
It's flexible rubber-like instead of stuff plastic-like.

You can also find "adhesive lined shrink tube":
https://www.google.com/search?q=adhesive+lined+shrink+tube
Looks like there's also "adhesive lined dual wall shrink tube":
https://buyheatshrink.com/heatshrinktubing/

Unfortunately, I don't have any experience with any of the
aforementioned adhesive shrink tube products.

--
Jeff Liebermann
150 Felker St #D http://www.LearnByDestroying.com
Santa Cruz CA 95060 http://802.11junk.com
Skype: JeffLiebermann AE6KS 831-336-2558