Have a look at the book "Sea Room" by Adam Nicolson. His son, Tom Nicolson, now owns the Shiants off Lewis. The land is grazed by the sheep of a Lewis crofter but otherwise I believe the islands are unoccupied and "available" for the sort of experiment you are describing. At one time they supported several families but at the time they became depopulated the inhabitants had shrunk to just one family. Your diet would become very monotonous; potatoes and fish mostly, and it would be very hard going but you might approximate to the sort of lifestyle you describe.