Process 4 cucumbers in food processor until smooth, stopping to scrape down sides. Pour through a wire-mesh strainer into a bowl, discarding pulp.
Stir 1/2 cup vinegar and salt into cucumber liquid; set aside.
Combine sugar and water in a small saucepan. Bring to a boil, stirring often; boil 1 minute. Remove from heat, stir in cucumber liquid mixture; set sauce aside.
Stir together soy sauce and next 4 ingredients in a small bowl; brush over salmon. Place salmon in a lightly greased 13- x 9-inch pan; sprinkle with sesame seeds.
Bake at 450° for 10 to 12 minutes or until desired degree of doneness.
Divide cucumber slices among 4 shallow bowls. Spoon cucumber sauce onto cucumbers and top with salmon fillets; add fresh mint sprig to each bowl, if desired. Serve with Ginger Vinaigrette.
