Cook rice according to package directions. Stir in vinegar, sesame oil, salt and sugar. Spread rice on parchment paper-lined baking sheet. Let cool completely. Refrigerate for 1 to 2 hours or until well chilled.
Using wet hands, press 2 tbsp chilled rice into 2-inch round cookie cutter; transfer to parchment paper-lined baking sheet. Repeat with remaining rice (you should have 24 rounds).
Heat 1/4 cup vegetable oil in large nonstick skillet set over medium heat. In batches, cook rice rounds for 2 to 3 minutes per side or until golden brown and crispy, adding oil to pan as needed. Transfer to paper towel–lined tray.
In bowl, stir together crab, mayonnaise, sriracha and sesame oil; refrigerate until ready to use. In small bowl, mash together avocado, lemon juice and salt; cover and refrigerate until ready to use.
To serve, top each crispy rice round with 1/2 tbsp spicy crab mixture and 1 tsp mashed avocado. Garnish with sesame seeds. Serve with pickled ginger, soy sauce and wasabi.
Alternatively, press rice into 2-inch square cutter, or use 2 tbsp to shape into ball, then press and flatten into a round. Repeat with remaining rice.