What about having a Fragile tag? A card that is Fragile will shatter if it is refreshed or repositioned or exchanged to opponent's hand via card effect.
This should be implementable NOT by having it be an effect that occurs on the play of the card itself, but by having the few cards that do cause such effects (a refreshed New tag, reposition within your hand, or exchange with opponent) have it coded into them to check for the Fragile tag and then, rather than draw the same card into the target position as would normally happen, place either a regular-draw card or a specific dummy card like "Broken shards" or something. (I recognize that passive abilities are not implementable, necessitating the alteration of the cards that cause the New tag to appear, not the target card.)