Roughly chop the salmon or trout, and combine it in a bowl with the remaining ingredients.
Set a heavy skillet over medium-high heat and add a drizzle of oil.
Shape the mixture into four patties and place them gently into the pan; cook until deep golden on one side, then flip and cook on the other side—they should cook through and be crusty and golden in 5-7 minutes.
To make the caper mayo, stir together the mayonnaise, lemon juice, capers and pepper.
Spread on the buns and top with salmon patties, tomato, lettuce and thinly sliced cucumber - and a little more caper mayo. Serve immediately.