All else being equal, I'd still rather hire the person that doesn't panic. I think it's entirely fair to subject a potential hire, especially for an important position, to a certain amount of stress.

Most people I know, myself included, have suffered from anxiety or panic attacks at some point in their lives. It's usually possible to overcome this, though. When you realize that you don't interview well, are afraid to speak in public, freeze up on dates, are afraid to speak to clients, panic when your boss disagrees with you, etc., you can either work on it or try to avoid those situations forever. Frankly, I'd rather not hire somebody who convinced themselves that they have to avoid certain situations because they can't handle them.

I do love the contractor idea, though. Perhaps it would be best to hire somebody as a contractor for a small project and then have them present in front of the entire team and ask specific questions or ask for live modifications?