Flake crabmeat with a fork in a medium bowl; stir in 1/4 cup mayonnaise, scallions, soy sauce, 1/2 teaspoon wasabi, and zest. Stir in 2 tablespoons breadcrumbs. Cover with plastic wrap; refrigerate 1 hour.
Meanwhile, stir together remaining 3 tablespoons mayonnaise and 1 1/2 teaspoons wasabi in a small bowl. Using a vegetable peeler, make 3/4-by-2-inch ribbons from cucumber (you'll need about 24 ribbons, or 1 for each cake). Fold each ribbon into thirds.
In a medium bowl, whisk together flour, salt, and pepper. In a small bowl, beat eggs with the water. In a shallow bowl, stir together sesame seeds and remaining 1/2 cup breadcrumbs.
Form 1 scant tablespoon crab mixture into a ball; dip in seasoned flour. Flatten into a 3/4-inch-thick disk about 1 1/4 inches in diameter. Repeat with remaining crab mixture. Dip cakes in egg mixture, then dredge in breadcrumb mixture.
Heat oil in a large skillet over medium until hot but not smoking. Add half the crab cakes; cook, turning once, until golden and crisp on both sides, about 1 1/2 minutes. Using a slotted spatula, transfer to paper-towel-lined plates to drain. Repeat with the remaining cakes, adding more oil if needed.
To serve, dot each crab cake with wasabi mayonnaise, and top with a cucumber ribbon and a piece of ginger.
To prepare in advance, cook the crab cakes as directed, and then let cool completely. Place on a baking sheet and freeze until firm, about an hour, then transfer to an airtight container and freeze up to 6 weeks. Bake, without thawing, in a 425-degree oven until heated through, 10 to 15 minutes.