Warm oil in a large skillet over medium heat. Stir in yellow squash and zucchini; cook for 10 minutes. Stir in shrimp and cook for 3 minutes. Stir in lemon juice, garlic, basil, oregano, salt, and pepper; cook for 2 more minutes.
Meanwhile, bring a large pot of lightly salted water to a boil. Add penne and cook, stirring occasionally, until tender yet firm to the bite, 8 to 10 minutes. Strain and pour into a large bowl.
Pour shrimp and sauce over penne, then sprinkle with chives and Parmesan. Stir to combine.