Then you must have a crap strap wrench. Or maybe your strap wrench is too large.
The other option would be to use a clamping thing and a cloth or something. But i wouldn't suggest this since you could damage the threads on the top.
EDIT: I just tried getting the top of my icd reg off with my strap wrench, and it worked with ease. My strap is about an inch wide, just wide enough to cover the whole part that goes inside of the asa.