Oldwizard is right. I've opened many weather proof boxes that were wet inside. I think the inside of your island would be considered a damp location and with flush boxes and in use covers and UF cable you would satisfy an installation under the definition of a damp location in the code.
From the NEC: Location, Damp. Locations protected from weather and
not subject to saturation with water or other liquids but
subject to moderate degrees of moisture. Examples of such
locations include partially protected locations under canopies,
marquees, roofed open porches, and like locations,
and interior locations subject to moderate degrees of moisture,
such as some basements, some barns, and some coldstorage
warehouses.
314.15 Damp or Wet Locations. In damp or wet locations,
boxes, conduit bodies, and fittings shall be placed or
equipped so as to prevent moisture from entering or accumulating
within the box, conduit body, or fitting.