Using rolling pin, smash whole cucumbers lightly, just enough to break open. Tear or cut into 1-1/2-inch pieces and season with salt. Transfer to sieve and let drain 10 minutes.
In large bowl, whisk vinegar, soy sauce, sugar, chili oil, and sesame oil; stir in grapes and scallions. When cucumbers finish draining, add to bowl with grape mixture and stir to combine. Sprinkle with sesame seeds and serve.