In reply to smithaldo:
I use 4mm accessory cord with a double fisherman's. It seems neat enough as the cord is relatively thin.
I don't think that knot strength is so much the issue - more about how easily it might work its way undone through regular use, which I've noticed is something that can happen to overhand knots in cord when e.g used as zipper pulls on packs or clothing. I don't think this will happen easily with a double fisherman's, or at least it's never happened with mine.
As far as I know the tethers are only rated to 2kn-4kn or so anyway (or sometimes not even sold as rated at all) and are not intended for any kind of weight bearing beyond securing the tools.
That said maybe a double fisherman's knot is bulkier when using thicker cord, but 4mm is rated to 4kn anyway and so the only reason I can think of to go thicker might be from a durability/longevity perspective. But the 4mm seems to be holding up okay so far after a few seasons of light use.
Post edited at 17:09