Seems to me that the khukuri gets its cutting power from its blade geometry, in particular the concave edge and rounded 'kissaki' (to use ths Japanese term; as I understand it, the part of the cutting surface that curves up from the edge to the point; very important, I believe, in cutting with Japanese blades)
Basically, I think, the khuk slices in and draw-cuts out; the angle and the curve follow the arc described by the human hand/arm in the action of cutting, so that sharpened edge is fed into the cut throughout the cutting process (unlike straight chopping blades, for example)
Accordingly, when using the khukuri, I try and pull it through what I'm cutting, like slicing up cheese with a cheesewire.