Maybe, but that's where some 'feel' and experience with the process comes into play. I'm sure the guys doing it this way, have been doing so for a long time. I have an oak strop block with some diamond paste compound on it, and I've started using a somewhat narrow elliptical motion on it, similar to the way many use a hard hone. Mostly lengthwise motion, parallel to the edge, but with a little bit of edge-leading and edge-trailing built in. It sometimes tries to bite in a little bit, but if the touch is light, I usually catch that before it digs deep. With my oak block, I've noticed it's much easier on this hardwood, aided by the fact that the wood itself has taken a bit of polish from the rubbing, and has become slicker in feel, much like a hard hone.
I've also used wet/dry paper on wood backing with an edge-leading stroke. Only issue I've had there, is the paper curls up at the edges, and the blade does catch that occasionally. I didn't use any means to stick it down, like gluing or wetting the paper, so that was my own fault. It does make one really pay attention to angle & pressure though, and that's one reason I like it. Great 'training aid' for good technique.