For the dressing: Simply combine all of the ingredients in a small bowl. Set aside in the refrigerator until you're ready to serve.
For the salad: Cut the melon in half, remove the seeds, and slice it into fairly thick wedges. Use a paring knife to remove the skin and then use a vegetable peeler to make very thin slices from each wedge. (You'll likely end up with a thicker slice that you can no longer make slices with -- just eat it!)
Cut a sliver off one side of the cucumber to make a flat edge. From this flat edge, use the vegetable peeler to create thin slices again.
In a medium-sized mixing bowl, combine the onion with the melon and cucumber slices. Pour the dressing on and toss it lightly. Add a bit of sea salt to each plate as you serve. This salad is best served chilled and within at least 15 minutes of adding the dressing.
Both Mirin and Yuzu juice can be found in Asian markets and often large grocery stores.