Thinly slice the avocado, cut the cucumber into matchsticks, and thinly slice the red pepper; set aside the carrots if not already matchsticked.
Thoroughly drain the tuna, then flake it with a fork into a large bowl.
Zest and juice the limes to obtain about 1/2 teaspoon zest and 2 1/2 tablespoons juice; add both to the bowl with the tuna.
Add the mayonnaise, Sriracha, and granulated sugar to the tuna; season with salt and pepper (about a heaping 1/4 teaspoon salt and 1/8 teaspoon pepper) and gently stir until combined.
Lay out the tortillas and divide the tuna mixture evenly among the 4 tortillas.
Top each portion of tuna with sliced avocado, matchstick carrots, cucumber, red pepper, and cilantro if using; finish with additional salt and pepper and a drizzle of fresh lime juice if desired.
Roll each tortilla tightly to form a wrap and serve immediately.