The strap and unintelligible onboarding are two reason why I gave up on the Twiddler. It’s really too bad because I love the idea and is in general very well executed, except for those two glaring issues.
I wish I had an answer to your question, but I love this idea. T seems that a leather strap would fit in the slot nicely and you could have something like a thin watch band which would allow different tightnesses for different size hands. Seems like a no brainer to me. I think a swivel stud with a flat loop might be the best option that would keep the strap flat and from cutting into your hand.
Good luck. I’m a buyer if you end up making more than just one!