I found it quite annoying that the hand strap keeps pulling the twiddler wrap off the device when taking on/off the twiddler. This is due to the fact that the strap is kind of riveted to the wrap at the bottom of the device, instead of the device itself. I changed that today, and in the process also got rid of the original strap which I find too sturdy and sweaty after a while.
It was kind of simple: open the Twiddler (thanks for making it so accessible!), drill a small hole in the back shell, insert a screw and tighten it with a nut from the outside.


I had an old fitbit strap, took a paper clip, bent it, soldered it shut to provide an eye and could mount this on top of the screw with two more nuts.




Fits my hand perfectly and is much easier to pull on and off my hand since, well, it's a wrist band anyway 🙂
YMMV. And yes, I void warranties.
Side effect: I can now also use the twiddler without the wrap. I thought about making the whole attach-detach-strap process with supermagnets, but didn't have any that would have served the purpose.