Hmm, I've never thought of who was on what contract as secret information.... In fact, when I've done new shows and Equity has come in to do the determinations (principals, specialties), we've been asked to post the list. Plus, once you start assigning understudies it becomes pretty clear as well...
In the past I've just had them gather on opposite sides of the same room after the AEA meeting, me with one group and assistant with the other, not so much out of secret but if I thought one group would be quick and the other not, or if I thought it would help them know who was/wasn't on their contract. Last show, we just did it all in one group at the end of the meeting.