I spoke directly with the warehouse today about Little Door for another magician. They said that if you make a note requesting a specific card that they will do everything they can to get you that card, but there are no guarantees.
You many not get the card you want for a few reasons, for any trick. It could be that the specific card you want is out of stock, or the packaging prevents the people at the warehouse from seeing the card you will get. There are other reasons of course, but in general if you need a specific card you can request it. Just be prepared, you may not get the card you want without warning.
For Mint Box by Daniel Garcia you can use any card you want as long as it has a red Bicycle Rider back.
I hope that helps.