I would be careful about any imigration cards and who you are sending this information to. The cruise line will check your documents upon boarding. Do not mail anything to any one prior to boarding. Call your cruise line if this is questionable information request.
You do not 'send' these forms to anyone. They will be collected when you board the ship to be given to the authorities in the Bahamas. That is their law and if you don't fill it out, you don't go. Each adult must fill it in if I remember correctly.
filling out these forms in advance just streamlines the check in process. They are simple forms, and if for some reason you do it wrong, the clerk at the check-in desk will give you another one to fill out.