In a small bowl, combine the cooked sushi rice with rice vinegar, monk fruit sweetener, and sea salt, folding gently to incorporate while keeping the grains intact.
Slice the sushi-grade salmon and cooked shrimp into long, thin strips; peel and slice the avocado and cucumber into matchsticks.
Place a nori sheet on a bamboo rolling mat, shiny side down, and spread half of the seasoned rice evenly over the bottom two-thirds of the sheet using damp fingers.
Arrange half of the salmon, shrimp, avocado, and cucumber in a horizontal line across the center of the rice.
Lift the edge of the mat closest to you and roll the nori tightly over the fillings, applying gentle pressure to create a firm cylinder.
Use a very sharp, damp knife to slice the roll into six to eight even pieces, then repeat the process with the remaining ingredients.
Serve the fresh rolls immediately with coconut aminos for dipping, a dollop of wasabi paste, and pickled ginger on the side.