Use small, slender Persian cucumbers -- they are less watery and have much smaller seeds. Korean hot-pepper powder is a blend of roughly ground sweet and slightly spicy red pepper. Chile de arbol is a good substitute.
Toss cucumbers with 1/2 teaspoon salt, and let sit 30 minutes. Transfer half the cucumbers to a clean dish towel. Fold the edges of the towel around cucumbers, and wring to remove excess liquid from cucumbers. Transfer to a large bowl. Wring out remaining cucumbers, and add to bowl.
Add red-pepper powder, sugar, scallions, garlic, 2 tablespoons sesame oil, and the vinegar. Massage seasonings into cucumbers; let sit 10 minutes.
Meanwhile, bring a large pot of salted water to a boil, and cook pasta until slightly beyond al dente (it should be very tender). Drain, and add to cucumbers. Toss to combine, then add remaining 3 tablespoons sesame oil and the soy sauce. Season with salt and red-pepper powder. Serve at room temperature.