Take a cab. It won't cost much and the hotel shuttles can't pick up from the port. My thought was for one person to take the cab while the other waits at the pier with the luggage. The one person at the hotel could bring the car back and get luggage. As a matter of fact, several drivers could share a cab to the hotel and bring the cars back.
If you are going to walk on thin ice, you may as well dance!
We've done a couple of things... whatever you do, don't even consider the Jet Express public transportation.
Taxi from airport to the Quarter was about $30 for up to two people if I recall correctly, if three or more people then about 12.00 per person.
Trip if you're staying at Holiday Inn Superdome it is a very cheap cab ride to the port like $10, maybe less. The last time we stayed there they had a free shuttle to the port, they just asked that you sign up for it the day before. It was pretty packed so we just cabbed it.