You know, I really read your thread as 'Wrist strap to tripod HEAD'.. So, you can imagine how curious I was about what you were trying to achieve.
Serious though, if its a small thread in there, why not scavenge an old tripod for the screw and hook the ring on that screw (with a washer if the screw head is smaller than the ring)?
A bit of locktite (the one that can be taken loose again) should keep it in place.