Combine rice and sesame seeds. Combine vinegar, sugar, and salt; stir to dissolve. Pour vinegar mixture over rice mixture; toss to coat. Set aside.
Stir together mayonnaise and cayenne; spread 1 tablespoon mayonnaise mixture over 1 tortilla. Spread 1/2 cup of the rice mixture on half of the tortilla; top with one-fourth each of the salmon, avocado, and cucumber. Carefully roll tortilla up tightly, starting at the filled side. Wrap in plastic wrap. Repeat with remaining tortillas, mayonnaise mixture, rice mixture, salmon, avocado, and cucumber. Chill at least 1, or up to 4 hours, before serving.
To serve, trim ends. Cut remaining roll crosswise into 1-inch-thick slices. If necessary, secure with toothpicks. Arrange on shredded lettuce, if desired. Makes 28 roll-ups.