Your participant shuffles the deck, then cuts a pile and counts them without telling you.
Your second participant chooses any card (completely free choice), and then you tell the participant to put the pile back on top the deck and give it a complete cut.
The Magician shows the audience that the cards are completely shuffled. Now your participant loses his card anywhere in the deck and starts dealing the cards one by one until the end. The last two cards total the reveal the number to count down to in the pile.
Finally collect the cards and deal that number to find the second participant’s chosen card.