Heat-shrink tubing available as a roll like adhesive tape?
Shrinking with heat makes no sense if its not a closed shape since it would pull apart since the heat activates both the shrinking and the adhesive.

If you are after rigidity and toughness then "silicone self adhesive tape", "self amalgamating tape", "self-fusing tape" (or some other name along those lands) will become hard. It looks like a roll of silicone tape backed with a transparent separate plastic to stop it from sticking to itself. It somewhat resembles something halfway between electrical tape and the the white teflon thread sealing tape. You should just be able to find it in a hardware store.

Do a test run on scrap and let it sit a day before you do it on the real piece so you know how it behaves while pliable and after it cures and how to best work with it. You do not want to have to go in and remove it if you mes up.

People who complain it wont stick flat on a surface are not using it as intended. It is meant to be STRETCHED and wrapped. I dont know what makes it hard but it does which surprised me too. It might be the mass fusing together to be thicker. Try it. I would rather remove heatshrink than this stuff. I have never been successful in excising it whereas heatshrink is dead easy hence my warning of a practice run.

Also, you realize your problem can be fixed using heatshrink with higher shrink ratios right?