Rinse the sushi rice under cold water until the water runs clear. Combine the rice and water in a medium saucepan and bring to a boil. Reduce heat to low, cover, and simmer for 18-20 minutes, or until the rice is tender and the water is absorbed. Remove from heat and let it sit, covered, for 10 minutes.
In a small bowl, mix the rice vinegar, sugar, and salt until dissolved. Gently fold this mixture into the cooked rice, then let it cool to room temperature.
Preheat the oven to 375°F. Lightly spray a muffin tin with cooking spray.
Take a wonton wrapper and gently press it into the muffin tin to form a cone shape. Repeat with the remaining wrappers. Bake for 8-10 minutes or until golden and crispy. Allow to cool.
In a medium bowl, combine the chopped shrimp, mayonnaise, and sriracha (if using). Mix well.
To assemble the cones, fill each wonton cone with a spoonful of sushi rice, followed by a layer of the shrimp mixture, avocado slices, and cucumber.
Garnish with sesame seeds and chopped green onions. Serve with soy sauce on the side for dipping.