A day or two before making the fish cakes, put the cod to soak in cold water. Change the water four or five times during this period.
Drain the cod and rinse it well under cold running water. Cover with fresh water in a saucepan, bring to a boil and simmer for 20 minutes or until cod is soft.
While the cod is simmering, cook the potatoes in their skins, then peel and mash with butter and milk.
When the cod is ready, drain it thoroughly and remove the skin and bones. Shred the cod with a couple of forks. Add the creamed potatoes, parsley, mint, pepper, egg yolks, and the port. Mix thoroughly. Whisk the egg whites until stiff, then fold into the cod mixture.
Heat the oil in a deep fryer or heavy deep pot to 375 degrees F.
Take a lump of the mixture, about the size of a small egg, and mold it in your hand to make a torpedo shape. Deep fry, in small batches, until crisp and brown all over. Drain on paper towels and serve hot.