Dragon Roll with Shrimp Tempura

Name: Dragon Roll with Shrimp Tempura
Ingredients: 2 cold large eggs, lightly beaten; 1 2/3 cups ice water; 2 cups all-purpose flour; 3 tablespoons cornstarch; Canola oil, for frying; 4 extra-large shrimp (about 8 ounces), peeled and deveined; Kosher salt; 1/2 cup Japanese mayonnaise, such as Kewpie brand, or regular mayonnaise; 2 tablespoons sriracha; 2 teaspoons dark soy sauce; Zest and juice of 1/2 lime; 2 sheets toasted nori; 1 cup cooked sushi rice, warm; 1 Persian cucumber, peeled and cut into 9 long batons; 2 to 4 ounces tobiko wasabi; Freshly grated wasabi and pickled ginger, for serving; Soy sauce, for serving