In a medium bowl, combine the drained tuna, mayonnaise, soy sauce, sesame oil, and sriracha (if using). Mix well until fully combined.
Lay a sheet of nori on a clean, flat surface or bamboo sushi mat, shiny side down.
Spread a thin layer of the tuna mixture across the nori, leaving about 1 inch at the top edge.
Arrange a few pieces of cucumber, carrot, and avocado along the bottom edge of the nori.
Starting from the bottom, carefully roll the nori over the filling, pressing gently but firmly to create a tight roll.
Once rolled, use a sharp knife to slice the wrap into bite-sized pieces. Wipe the knife with a damp cloth between cuts for cleaner slices.
Repeat with the remaining sheets of nori and filling.
Sprinkle sesame seeds over the wraps for garnish before serving.