I think shrink-wrapping a Flight Case might be a bit of overkill -- an instance of running without being chased. Also, at least with the delicate model I've just made, it could mess up the workings.
Here's a handling of Flight Case I just tried out on some humans over the weekend to great effect:
Starting with a normal deck in a normal case, I removed the deck and tossed the case into my backpack off to one side.
Thumbing through the deck, I said, "Oh, this still has one of the Jokers. I don't use those." I removed the Joker, reached into my backpack, and removed the Flight Case. I opened the box, casually letting folks see inside. The only thing visible was the "other Joker." I put the Joker inside the box, closed it, and then absent-mindedly left the box out in full view.
I launched into the Ambitious Card, a four-ace routine, and some other stuff. When it was time for the finale, I "failed" to reveal a selected card, instead producing the one that had served as the Ambitious Card. Setting it aside face down (after first switching it for the true selection), I commented -- as if making a face-saving ad lib -- that that old selection keeps popping up even when uninvited.
I resumed shuffling and then said I had a better idea. I asked the spectator to hand me the card box. Then I set down the deck and placed the tabled card (still face down) on the box. I said I would try to make the card "embody the spirit" of the correct selection. It levitated mysteriously, after which I had the spectator remove it and confirm that it had now changed to the selected card. Under cover of this surprise, I ditched the Flight Case in my backpack. No one asked to inspect it, and if they had, I would have brought out the original case.
With this handling, spectators actually had a look inside the Flight Case, viewed it for many minutes, handed it to me, and removed the levitating card from it. And under cover of the surprise revelation, the case was ditched without comment.
I was never much of a fan of close-up levitation effects until now.