There are morgues on most cruise ships.
Should the morgue fill up, only then will they use one of the fridges/cool rooms.
They do not put bodies in the freezers. And they do not put bodies alongside produce.
The room used has to be completely fumigated after it has been used to 'store' a body.
QE2 has a morgue for six bodies. They ran out of spaces once and had to use a store room.