To be honest I usually use the CL with either a wrist strap or the original black neck strap, but my Domke Gripper strap also fits just fine with the split rings removed from the ends. Just make sure you get the 1" version and not the 1.5" - I think the strap ends on the 1.5" version are thicker. I actually bought the Domke for my Konica Hexar AF, which seems to have even narrower lugs than the CL, so you could see if there are any threads discussing this issue with the Hexar AF.
Mark