Bring a large pot of heavily salted water to a boil. Cook orzo until al dente. Drain and run cool water over it until it's cooled.
Make the dressing. In the bottom of a large bowl, mix shallot, vinegar, maple syrup, Dijon, and ½ teaspoon oregano. Slowly stream in 4 tablespoons oil, whisking constantly. Season to taste with salt and pepper and set aside.
Pat shrimp dry with a paper towel. Season with remaining 1 teaspoon dried oregano, salt, and pepper on both sides.
Heat remaining 1 tablespoon oil in a large skillet over medium-high. Add shrimp and cook until pink and fully cooked through, 2-3 minutes. Remove and set aside.
Add the cooled orzo, cooked shrimp, green onions, tomatoes, feta, cucumbers, and dill to the large bowl with the balsamic dressing. Season to taste with salt and pepper. Toss to coat and serve immediately.