Place garlic scapes, Romano cheese, parsley, and walnuts in the bowl of a food processor; pulse to combine. Scrape down sides. Turn on food processor; pour in olive oil and lemon juice while processing pesto until smooth.
Fill a large pot with lightly salted water and bring to a rolling boil. Stir in pasta, bring back to a boil, and cook over medium heat until tender yet firm to the bite, about 11 minutes. Drain and transfer to a large bowl.
Stir pesto and shrimp into the pasta. Season with salt and black pepper. Squeeze a lemon wedge over pasta and serve remaining wedges alongside.