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I'd have never tought I'd ever answer this in a Bitcoin forum, but what a funny thing; iy's going to happen. I'll try to give the short answer tough.
Legal lines are defined based on the distance from the coastline; so you have 3 different zones before reaching international water: coastal water, territorial waters (coastal to 12 miles) and the Economic Exclusive Zone (EEZ) (12-200 miles). I'm also writing this by heart in the middle of a lecture, so some definitions may change a bit from the actual ones; but that's not the point...
Since coastal and territorial waters are the one real close to shore, they are of no importance to this thread, except for when the ship is going to port. This cruise will most likely operate on International waters. Taxes and law enforcement agencies can still board your ship and even detain it inside the EEZ, and that wouldn't be very good for our felow crypto enthusiasts.
Once outside the EEZ, International waters, the laws and regulations from the flag state are still applied; and are actually the only ones applied and are enforced mostly by the crew and any private security that may be hired. It's the closest one will ever get when a captain was the judge, police and a couple more things; that no longer happen in practice. There's a small issue I see to this tough; and it's the actual depth of the international waters.
Many people may not be aware of that, but ships can't actually anchor anyway; the lenght of the required chain to anchor in a 400 meter depth area would be too big, with the weigh that would have, so ships can only anchor in rather shallow areas. Knowing that, I'm prone to believe that the ship would be left adrift most of the time, which raises a couple of flags inside of me from a navigational security standpoint. Fuel consumption will be huge too; so some sort of hybrid clean energy plant would be a great idea to reduce the amount of electricity that the diesel generators would need to produce.
And even if this last part is mostly speculative, I can always be corrected; because we are all here to learn new stuff (or at least I hope so).
PS: Starting to speculate.... setting up a mining farm close to the keel might be a good idea here. The only downside is that the electricity would be supplied by the generators (and that costs fuel), and that the satellit internet is not usually the best of the best. Otherwise, you have a huge area that would have a great natural refrigeration system; you could just set up some lines and with a "small" pump, keep the water running so that it never overheats...