If you purchase transfers from the cruise line it makes no difference if you come in the day before or ten days before. You can purchase transfers without having cruise air. You just have to meet them at the airport. I did this one time a few years ago on NCL when we cruised out of Dover, England. We came in two days early and then did an airport transfer.
The representatives will be in the "unsecured" area of the airport. We spent a little while looking for them and lugging our bags around. Once we found them we just went out, gave our luggage to the bus driver, boarded the bus and off we went.
If you want to do this then contact your agent or the cruise line and purchase an airport transfer.
Just remember, it may be less expensive and less hassle to just take a taxi to the port. The cruise line transfers charge per person and a taxi is per car. In Miami or Fort Lauderdale a taxi is less expensive if you aren't staying too far from the port.