Slice the sashimi-grade tuna with a sharp knife into very fine, uniform cubes. Halve the cucumber lengthwise, scrape out the wet seed cores if desired, and slice the flesh into thin half-moons. Slice the scallions into fine rings and set these aside together with the soaked wakame for use.
Make a dressing by thoroughly stirring together the soy sauce, sesame oil, rice vinegar, and wasabi in a large bowl until the wasabi is completely dissolved in the liquid. Add the sliced tuna cubes to the bowl. Gently toss everything together so the fish is well coated with the mixture and let it marinate briefly.
Divide the sliced cucumber and wakame as a base over two chilled plates. Spoon the marinated tuna tartare into the center on top. Finish the dish by evenly sprinkling the sesame seeds and finely sliced scallions over the tartare and serve immediately.