Rehydrate the wakame: cover the dried wakame with warm water and let sit 5 minutes until unfurled and deep green. Drain well, squeeze out excess water, and roughly chop long strands into bite-size pieces.
Slice the cucumbers paper-thin: trim the ends, then slice into 1/16-inch rounds with a sharp knife or mandoline.
Salt and rest: toss the cucumber slices with the teaspoon of kosher salt in a colander set over a bowl. Rest 15 minutes at room temperature so excess water drains away.
Squeeze dry: take handfuls of the salted cucumbers and squeeze firmly to wring out as much water as possible, then transfer to a mixing bowl.
Whisk the dressing: combine the rice vinegar, sugar, soy sauce, and salt until the sugar fully dissolves.
Toss and chill: pour the dressing over the cucumbers, add the wakame, and toss to coat. Cover and refrigerate at least 10 minutes before serving.
Serve: transfer to small bowls, spoon over a little dressing, and finish with toasted sesame seeds and the optional sesame oil and scallion greens. Serve cold.