Peel the kani. Press each from tip to tip between your fingers. Pull apart to shred.
Thinly slice the cucumbers and carrot, and julienne (cut into matchsticks).
Cut the mango; discard the stone. Slash diagonally, the slashes about a quarter inch apart, all the way but without cutting through the skin. Using a spoon, scoop out shallowly to come up with thin strips.
Rinse the lettuce and dry in a salad spinner. Cut the leaves horizontally into half-inch slices.
Place the shredded kani, julienned carrot and cucumber, sliced mango and lettuce in a mixing bowl. Drizzle in the sesame seed oil. Toss to distribute the ingredients evenly. Use your hands to toss to avoid bruising the ingredients.
Add the Japanese mayo. Toss the kani salad once more to moisten everything evenly.
NOTE: There is no need to add salt. The kani is sufficiently salty to blend perfectly with the sweetness of the carrot, cucumber and mango.