Pretty sure it can be made such that the edge doesn't contact the cardboard. Wrap around the back of the blade and long enough that the point is protected. The handle should allow the cardboard to stay in place.

Something else to consider if you want high tech is to pick up a few of the very strong neodymium magnets, enough such that they can pinch the cardboard to the carbon steel blade. Duct tape the magnets and the cardboard should stay in place nicely. Haven't done that but it works great in my mind