Bring water, wild rice, and salt to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until rice is tender, 30 to 45 minutes. Drain excess liquid, fluff rice with a fork, and cook uncovered 5 minutes more.
Bring a large pot of lightly salted water to a boil. Cook orzo in the boiling water, stirring occasionally until tender yet firm to the bite, 7 to 10 minutes. Drain.
Melt 1 tablespoon butter in a large nonstick skillet over medium heat. Add onions; cover and cook until translucent, about 5 minutes. Stir in remaining 2 tablespoons butter, peas, salt, and pepper. Cook and stir until combined, about 1 minute more.
Pour rice and orzo into a serving dish. Stir in the pea mixture and green onions.