I've got one of these https://www.ebay.com.au/itm/Blue-Wid...UAAOSwstxVLSsx
from schlepping an EOS 1D with a big zoom around racetracks, the length of the nylon ends seems to keep the wide bit just clear of anything you want to do on the camera, and they're thin enough to grip over (eg to keep the rest from dangling in your face if you've your eye glued to a viewfinder doing portrait shots of Every Single Trackday Participant At The Same Bloody Corner) while the wide (cotton, feels nice!) bit is wide enough to never tangle. Makes a good makeshift wrist strap too by doing a few loops for that very reason.
another one I like is the original (p?)leather thin (~1-1.5cm wide) strap with a sliding pad that came on a Pentax SP500 (spotmatic): it's super supple and never got in my way (admittedly didn't use the camera much) but I can directly compare it to the same vintage (p?)leather strap of identical dimensions from my OM1 which has gone quite stiff and unruly, much more of a pain to handle. Both seem (to me) to have enough "depth" (they're folded over and stitched down the middle) to be minimally tangleable, but YMMV.