All you really need to change is the skewer. The trainer puts a lot of stress on skewers and eventually the skewer can break, which isn't much of a big deal if you're on the trainer, but if you're out there on the road that could spell disaster.
I wouldn't be too worried about actually having the wheel itself on the trainer (with a different skewer), but if you have a set of backup wheels then why not use them to be safe? It doesn't really take much more effort to change the entire wheel than it does to change skewers.
Whatever you do, just don't use the skewer that you use on the trainer out there on the road.