Make crackers: Pour enough vegetable oil into a 6-qt. pot to come at least 1 in. up sides. Heat over medium-high heat to 350° on an instant-read thermometer. While oil is heating, brush 6 nori sheets with beaten egg and top with remaining 6 sheets. Cut each in half. When oil is hot, fry 3 pieces nori at a time until crisp, 2 to 3 minutes. With tongs, transfer to a rimmed baking sheet lined with a cooling rack. Fry rest of nori the same way.
Make aioli: In a blender, blend garlic, lemon juice, and yolks until well combined. Add salt and, with motor running, drizzle in 1 tbsp. cold water, followed by rice-bran oil in a thin stream. If it becomes very thick, add a few tbsp. cold water to make a loose, creamy sauce and to keep it from separating. Whirl in 1 tbsp. each Sriracha and tamari, taste, and add more if you like.
Make poke: With a sharp knife, cut tuna into 1/4-in. dice and put in a large bowl. Drizzle with tamari and sesame oil. Gently mix with your hands and add more tamari and/or sesame oil to taste. Mix in green onions, ginger, and chile.
Spoon poke onto crackers and top with a few drops of spicy aioli. Sprinkle with radishes, shiso, sprouts if using, and sesame seeds. Serve with more aioli on the side if you like.
*Find dried nori seaweed on the international aisle of your grocery store, and shiso at Japanese and specialty produce markets. Tuna is among the safest of fish to eat raw--it's not prone to parasites--but buy it from a good market that knows how to handle it.
Make ahead: Nori crackers, up to 1 day, stored airtight. Aioli, up to 2 days, chilled.
Note: Nutritional analysis is per cracker.