If your flying to another EU destination then you cannot take any duty free with you. If it is a non EU destination then you can.
In my experience whilst on the cruise ship I have placed an order on board and the items are delivered to your cabin the day before you dock. You could trying buying items in the places you visit but I have heard of some cruise lines not allowing this ( they want you to buy booze etc on board)
When we did our northern lights cruise in Norway in February this year, a number of people bought bottles of alcohol in the duty free shop at the airport in England just before boarding the plane to Norway. I don't know what people did on the way home.
We didn't bother buying anything from the duty free shops in either direction.
NCL and Royal Caribean wont let you take alcohol on board at all, the logic is the same as planes so they can control the alchohol levels of passengers so they dont go overboard (weak i know). QM (Cunard?) will let you but it has to be of a sensible level and to be drunk in the cabin.