In a large bowl, whisk together tamari, 1 tbsp vinegar, oil, garlic, honey and Sriracha. In a separate bowl, toss together cucumber, carrots, radishes, scallions, remaining 3 tbsp vinegar and salt. Let stand 10 minutes, tossing occasionally.
Bring a large pot of salted water to a boil. Cook spaghetti as directed on package until al dente. During the last 2 minutes of cooking, add shrimp. Drain noodle mixture and rinse with cold water, shaking out any excess. Add noodle mixture and vegetables to bowl with tamari dressing and toss. Top with sesame seeds.