I doubt you would ever need something as aggressive as a scythe stone to bring the edge back up on an HI khuk. I don't know if your familiar with scythe blades but they are very thin. Machete like. Well at least the ones of many moons ago. I used to talk with the guys in the sub-forum over in the axe forum about my old scythe and stuff. You could sure use the stone though, it would be just like any other stone except it would fit the contour of the blade. The stone would work fine, it would just put a rough edge on the blade first then take quite a bit of honing to get it back to fine again.
I normally use round ceramic rods or sand paper when I know I'll need to touch up out and about.