Shrink tubing is fine to use to insulate wires. Not sure exactly what you have, but if you feel it is too thin as some have suggested, use multiple layers. As for it making you wires too stiff, you can shrink it in place - after all, you are not going to be trying to use it to help you weld some irregular structure.
As for the adhesive
, i.e., if you want it, there are many on the market that will stay flexible/not crystallize for many, many years - if ever. I will let others make that suggestion.
For whatever it's worth, although it was some years ago, I worked as a senior R & D lab tech for a company that manufactured only heat shrinkable products.