Reptiles should always be shipped overnight/next day. 'Out of the water' is irrelevant, but access to drinking water would be the issue--Most reptiles can safely go a couple of days without water, some can go longer.
You will need to find a shipping service that accepts crocodilians--I'm not sure that something like Delta Dash isn't the the only choice. You may need a specially approved box, depending on the size of the animal. Always ensure that it is legal to ship an alligator to the destination you intend to ship to.
If it's small enough to be shipped via the typical delta dash/fedex route, there will be no problem.
If the gator is big enough that it can't be moved through the typical means in the herpetoculture hobby, I would consult a local zoo with crocodilians for advice on moving large water-based reptiles.