If you lower your wrist, so it is more in line with the razor, you will not have the pressure problem.

Try to use, just enough pressure to keep the razor flat, on the strop.

In the video, the stropping looks a bit awkward, because he is holding a paddle strop in midair.

It would probably look more relaxed with a hanging strop or the paddle on a flat surface.

With this technique, the only thing moving, at the flip, is the thumb. The concern is the pressure at the flip, slamming on the strop. You can control the torque on the razor with the thumb.