Put a large pot of water on to boil for the pasta.
Meanwhile, prepare sauce: Place parsley, garlic, lemon juice, oregano, crushed red pepper (if using), salt and pepper in a food processor. Puree until smooth. With the motor running, drizzle in oil. Scrape down the sides, then process again until well combined. Place 2 tablespoons of the sauce in each of 4 small lidded containers and refrigerate. Refrigerate any remaining sauce separately for another use.
To prepare noodle bowls: Cook spaghetti in the boiling water according to package directions. Drain and rinse under cold running water, then drain again and transfer to a large bowl; add zucchini noodles.
Using tongs or two large forks, gently toss the spaghetti and zoodles together until well-combined. Divide among 4 lidded single-serving containers. Top each with 3 ounces shrimp and 1 tablespoon feta.
Seal the containers and refrigerate for up to 4 days. Toss with chimichurri sauce just before serving.
