So I have you have the magic creator on the team. Why not use the start of magic mulligan. Discard hand, reshuffle, redraw one less card than you did last time. Repeat one more time if necessary.
That would prove difficult as you don't draw that many cards to begin with and may be problematical for the AI to judge their hand.
Its an interesting thought, though I don't know if the added fiddliness would be worth it. Also, in magic one of the main issues mulligans helped with was not drawing a usable land / spell mix. The analogous situation would seem to be moves / non-moves in CH, and that's smoothed out somewhat already by the bonus move cards.
I would say that losing a card is out, as you draw so few cards in the first place. Instead one could simple have one single opportunity when the match first starts to redraw your opening hand. The drawback is of course that you could possibly draw an even worse hand and then be stuck with it. One would have to weigh whether their opening hand is so bad that a chance at a better redraw is worth it. The AI would just never mulligan.
im not saying that this would be something that would be used often. but every now and then i seem to get an opening draw with 3 movement cards on my dwarf warrior. id be willing to take one less card to not have to play out a game that i know is going to be a loss.
This makes good cards and bad cards more valuable to mix as you can secure your self from a screw early i highly disapprove.