Big Head Zach
Without looking at the rules, I'd argue the opposite. Showing the cards to an opponent is a price you have to pay for the privilege of using the ability on the card. If you don't have any cards, you can't pay that cost. Especially as this is one of the strongest cards in Caprice's deck. It's bad enough that you can immediately discard the 2 cards that you showed to pay for the powerful card that you just drew.
I don't think that's the timing of discarding cards for a discount. I'd think they get tossed before the card's text takes effect.