I think any small, adjustable strap will work. The GR is so small and light you can get away with nearly anything - I agree using "mirrorless" in your search terms will provide you with all kinds of results, from small leather straps, to braided and everything in-between. If you've a camera store nearby, you might go in and see what's available locally.
Also remember - you can shoot a K1 with smaller apertures and with a mind for composition just as easily as you can with the GR.
added:
I've got a great strap from DSPTCH that came with a TLR i was given a few months ago that I didn't like at first but have grown to love quite a bit for its simplicity (I've the regular sling, olive olive color). Their stuff isn't cheap but it isn't pricey either and its quite well made. Nylon, paracord - quite a few options... and the nice part is you can pick up additional connector to attach to other similarly-weighted camera bodies and switch the strap to carry those in just a couple seconds.
https://www.dsptch.com/collections/straps
(I can also confirm that the "Round cord 1/2" connector (Pair)" will fit just fine through the very small strap-loops of the GR)