Remove all skin, pin bones, blood lines and sinew from the snapper fillet. Slice the fillet lengthwise into long strips about 1/2-inch wide and refrigerate until ready to use.
Whisk together 2 tablespoons of the mayonnaise with the sriracha in a small bowl. In a separate small bowl, whisk together the remaining 3 tablespoons of mayonnaise with the wasabi paste and a splash of water if needed to loosen the mixture. In a medium bowl, gently combine the cooked sushi rice with the vinegar.
Lay a piece of plastic that is bigger than the nori sheet on a clean work surface. Lay a nori sheet on top of the plastic in the center. Dip your fingers in water as needed to keep them from sticking to the rice, then use your fingers to spread 1/2 cup of the sushi rice evenly on the nori sheet and gently press down. Flip the nori sheet over so the rice is face down.
Spoon about 2 teaspoons of the sriracha mayonnaise horizontally across the center of the nori sheet. Place 2 strips of snapper on top of the mayonnaise, then top with a strip of cucumber and 4 to 5 slices of avocado. Using the plastic wrap as a guide, roll the sushi as tight as possible into a log. Trim any excess nori as needed. Remove the plastic and use a sushi mat to form the sushi into a uniform round roll with a flat bottom. Repeat with the remaining ingredients to assemble three more rolls.
Cut each roll into 6 to 9 pieces. Use a spoon to smear about 1 tablespoon of the wasabi mayonnaise on one side of the serving plate. Place the sushi on the other side of the plate, then sprinkle with some of the furikake. Place about 1 tablespoon salmon roe on top of the wasabi mayonnaise and garnish the plate with a splash of toasted sesame oil. Serve immediately with pickled ginger, soy sauce and wasabi paste.