Amazon, to my shame.
Coycoye 750 Pieces Heat Shrink Tubing, Electric Insulation Heat Shrink Wrap Cable Sleeve, Cable Insulated Sleeving Tubes, Shrink Ratio 2: 1, 5 Colors https://amzn.eu/d/j6092aj
Bought a few years ago for a job, then lost and only recently found again. Handy stuff. Added another layer, which will either do a great job or turn into a bubbling molten mess and stick the mug to my beard.

I think that might melt as I doubt it'll be flame proof. Ideally, silicone tubing.

You might be right. Test later, will report back.

Test done, and the verdict's in.

Heatshrink: looks pretty, and pleasing to apply, but doesn't withstand flame from stove and is still too hot to the touch.

MSR panhandler: foolproof but a touch bulky.
Silicone grip from the kitchen drawer: also bulky, but will stop stuff rattling around in stead of a buff and is what I'll take once I've scraped the rubbery plastic mess off the handles.

I did my handles with red heat shrink - works very nicely
Edit…. Noticed the burn at the bottom. Make flame smaller and doesn’t happen.
Tricky with with meths burner I know (I use gas so usually set flame to no larger than mug diameter)

Good to know it can work. The use of bio-ethanol may or may not have been a factor too.

Sugru, used on the meths stove and gas

Cool. Used to have some but it went off. Will source more. That looks great.

Used the pot I’d added heat shrink tubing to today. Didn’t burn my fingers so I guess I’d call it a success so far. I use an MSR Pocket Rocket so don’t have as much of an issue with errant flames melting the tubing.