Check-in is not actually at the Hyatt desk, but in the lobby. There's a table set up with two cast members sitting at it. There are plenty of other cast members in the airport concourse, wearing blue blazers, directing passengers to busses, as well as DCL signs on easels all over the place. It shouldn't be hard to find.
Since this is kind of a special circumstance, you might want to talk to DCL reservations about this....