Cook the soba noodles as per the instructions on the package. When done, drain, run under cold water, and set aside.
In a small bowl, whisk together the sauce ingredients until well combined. Transfer the soba noodles back to the pot they were boiled in (or to a mixing bowl) and drizzle half of the sauce over the noodles; toss to evenly coat the noodles.
Add the drained salmon, cucumbers, edamame, and scallions to the noodles. Drizzle the rest of the sauce over the contents; toss to coat, while also mixing all of the ingredients into the noodles.
Evenly distribute between two bowls and garnish with sesame seeds.