That should be correct. The chocobo that was last assigned to your whistle will still be on it when you get it recharged.
However, if you decide to (or accidentally) get another chocobo onto your whistle, you should be able to re-assign a chocobo to it by trading the VCS Registration card you get from the CRA person when you retire the bird, and selecting that option. You can also get chococards for that bird using the same method if it's been retired already.
Personally, I keep all cards in the storage space the related plaque makes available -- like keeping the card under the plaque... but not. It just makes me feel better thinking it's safe there though
