Form the mixture into six 1-inch patties and chill for 30 minutes.
In a small bowl whisk together the mayonnaise, wasabi, and lime juice. Cover and chill.
In a medium bowl combine the cucumber, red onion, pickled ginger, and rice vinegar. Toss to coat and season with salt and pepper.
Heat a dry large heavy skillet over moderately high heat. Brush each tuna pattie with the vegetable oil. Cook the tuna patties for 5 to 6 minutes per side until they are just cooked through. Transfer the tuna patties to the buns and top with the wasabi mayonnaise and the pickled cucumber ginger relish.
Recipe courtesy of Gourmet Magazine