Alternately peel a ½ inch (1.3 cm) wide strip lengthwise, leaving a strip of the skin intact. With this method, the cucumber slices have some decorative dark green accents and a little bit of extra crunchiness. Cut the cucumber into small pieces (I use the Japanese cutting Technique called "Rangiri").
In a small bowl, soak the dried seaweed in warm water. Let it soak for 15 minutes. Drain and squeeze the liquid out. Set aside.
In a medium bowl, combine all the ingredients for the vinaigrette.
Add the cucumber, octopus, seaweed, and sesame seeds and toss them all together. Chill in the refrigerator for 30 minutes before serving.
You can keep the leftovers in an airtight container and store in the refrigerator for 2-3 days.