How long can I go without wearing my Invisalign tray?

When you get home to put the new trays in you might find them tighter then usual. Your dentist would probably suggest you wear them for longer time then your usual schedule to make up for the lost time. You should check with your dentist when you get back if the new tray doesn’t seem to fit properly. 

Put the new trays in as soon as you arrive back home. Wear them a few extra days and everything should be fine. Call your dentist or orthodontist and let them know what has happened and re-schedule your next appointment for a few days later than you are already on the book for. You're in a beautiful part of the country. Enjoy your vacation and the boat ride back to civilization.

While not ideal, a mere 2 days without aligners shouldn't make a big difference.  It may result in wearing the next aligner for additional days to compensate, but should be fine in the big picture.