Before spending a lot of $$, it’s worth checking out the optical properties of the plastic that the tube is made of (unless you’re thinking of drilling holes for the LED’s). My investigations didn’t look that promising when trying to ascertain that the plastic was transparent to IR wavelengths. When I use a thermotex around a tube, most of the heat I can feel is from contact with the tube (which absorbs the heat) rather than radiant heat.
If you buy a couple of those wrist bands and take them to pieces, there’s a good chance that you could create something that will fit inside the tube, but it would be a bit Heath Robinson.