Whisk together the soy sauce, orange juice, lime juice and rice vinegar in a shallow bowl. Dice the tuna into small cubes and place into the marinade. Cover and refrigerate.
To make the rice cakes, stir together the cooked sushi rice, bread crumbs, mayonnaise, miso paste and scallions. Wet your hands and form the mixture into 4 large balls.
Heat oil in a skillet over medium-low heat. Place the rice balls into the skillet and press down with a spatula to flatten. Fry until golden on each side. Remove onto a paper towel-lined plate.
Using a vegetable peeler, remove the skins from the cucumber and carrot. Run the peeler down each vegetable to create ribbons.
To serve, place one rice cake on a dish and top with tuna, vegetable ribbons and furikake.