Whether you switch carriers in the mission or not, it would appear that, if you have bought SC, you still get access to the advanced ATC radio comms, the "pop-up ball" and ED's LSO grading, so if that was all you were looking for, then just carry on using the existing mission, with the Stennis.
Having said that and even though the deck crew don't yet do anything for recoveries, I still hope that someone produces an SC variant of the mission, just to see a more lively deck.