Soak wakame in water for 10 minutes to re-hydrate. Drain well and transfer to a bowl.
Alternately peel a ½-inch-side 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 cucumbers into thinly slices, about ⅛-inch thickness (or even thinner).
Sprinkle the cucumber slices with salt and massage them. Let stand for a few minutes and squeeze out excess water from cucumber. Transfer to the bowl from the first step.
Combine the dressing ingredients in a small saucepan and cook over high heat until the sugar dissolves completely. Set aside to cool.
Before serving, pour the dressing over cucumber slices and wakame and mix well together.
Serve in individual dishes and garnish with ginger on top.