Rather, a good solution would involve deriving a (site-specific) token from the fingerprint and handing it off to the remote service, which then deals with it in much the same way we expect sites to deal with passwords.
This, of course, presupposes that we can retrieve a consistent and unique fingerprint from the same iris from various different images of it, and breaks down if all we can do is check an iris image to see if it matches a fingerprint.