Folks,
The edifice located at 1 Centre Street is the
Municipal Building which all of you must have temporarily forgotten. I say this only so that OP doesn't start wandering around.
OP,
I'm not saying this is impossible, but it does seem difficult. The
Marriage Bureau has notoriously long lines to the point of newspapers running stories on the problem at least once a year. (A new city initiative is underway to shorten the wait.)
You need to clear security in the Municipal Building. Then you need to clear security in the Supreme Court building (60 Centre Street, the building shown at the opening of "Law and Order").
I am an attorney although I do not practice domestic relations law. It would seem to me that a "judicial waiver" is one that is signed by a judge. I think expecting to see a judge and leave with a signed order in one hour is very unrealistic barring some emergency circumstances. I'm not saying I never accomplished this only that the number of times it happened were few enough to call it rare.
Incidentally, I am not even considering what the law says the grounds are for the judge to grant or deny such an order.
Good luck.