Cut zucchini into noodles using a spiralizer fitted with the large shredding blade.
Saute cherry tomatoes, snap peas, sweet peppers, and onion in a large saucepan over medium-high heat until tender, about 5 minutes. Add garlic; cook until softened, about 2 minutes. Remove from heat and place vegetable mixture in a bowl.
Return saucepan to medium-high heat; add shrimp and chile paste. Saute until shrimp begin to turn opaque and is coated in paste, about 2 minutes. Add vinegar; cook until reduced, about 1 minute. Add vegetable stock, fish sauce, and sesame oil. Add the vegetable mixture and zucchini noodles. Cover and allow zucchini to steam, 2 to 3 minutes. Season with salt and pepper.
Split the zucchini between 4 plates. Top with the shrimp, vegetables, and broth. Finish with green onions, cilantro, and lemon zest.