You could look at the corner types that actually arise in the aperiodic edge-tilings you mention and thereby find small collections of corner-tiles with analogous aperiodic tilings, using the method in my answer to your previous question, which converts edge-tilings to corner-tilings and vice versa. That is, which combinations of corners arise in the aperiodic tilings in the small edge-tile sets that are known? The answer would tell you which kinds of tiles are needed in the translation and thereby provide a upper bound for an answer to your current question.

You could look at the corner types that actually arise in the aperiodic edge-tilings you mention and thereby find small collections of corner-tiles with analogous aperiodic tilings, using the method in my answer to your previous question, which converts edge-tilings to corner-tilings and vice versa. That is, which combinations of corners arise in the aperiodic tilings in the small edge-tile sets that are known? The answer would tell you which kinds of tiles are needed in the translation and thereby provide a upper bound for an answer to your current question.