Make the wasabi aioli: Combine wasabi powder, orange juice, lime juice, 1 tablespoon pickled ginger in the bowl of a mini food processor, or mortar and pestle. Puree or grind until completely smooth. Scrape the mixture into a bowl. Add 1-cup mayonnaise and mix well to combine. Refrigerate the aioli until ready to use. You will have more than you need, but it will keep for up to 2 weeks refrigerated.
Make the relish: Combine the cucumber slices, red onion rings, rice vinegar, sugar and 1/2 teaspoon salt in a bowl; toss to combine. Set aside at least 1 hour. Or refrigerate up to 1 day before using.
Make the burger mixture: Pulse the tuna in a food processor 12 or 15 times, scraping down the sides halfway, to create pea-sized pieces. You may alternatively use a chef's knife. Scrape the tuna into a large mixing bowl and add the diced red onion, remaining pickled ginger, chili paste, soy sauce, sesame oil, remaining 2 tablespoons mayonnaise, Panko breadcrumbs and a pinch each of salt and pepper. Blend well and form into 2 one-inch thick patties. Place on a plate and refrigerate, covered for at least 1 hour and up to 3 hours. Lightly oil a cast iron or non-stick skillet and then heat it over medium heat. Gently lay the tuna patties onto the heated surface. Let them cook undisturbed, about 3 minutes until browned on one side. Flip and cook an additional 3 or 4 minutes until barely cooked through.
Make the burgers: Lay the buns out on a work surface. Put a small amount of sprouts on the bottom halves, then some of the Japanese cucumber relish. Top each with a tuna burger, then spread a bit of the wasabi aioli on top of them. Cover with bun tops and serve.