Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until tender but still firm to the bite, stirring occasionally, 6 to 8 minutes. Drain and reserve about 1 cup of the pasta water.
For the vinaigrette: In a small bowl, whisk together the olive oil, lemon zest, lemon juice, salt and pepper until smooth. Set aside.
In a large skillet, heat the oil over medium-high heat. Add the shallots and cook until soft, 2 to 3 minutes. Add the shrimp, salt and pepper. Cook until the shrimp turn pink and are cooked through, 2 to 3 minutes. Remove the shrimp from the skillet. Increase the heat to high. Add the wine and arugula. Using a wooden spoon, scrape up the brown bits that cling to the bottom of the pan. Cook for 1 minute until most of the liquid has evaporated and the arugula has wilted. Add the cooked pasta, cooked shrimp and vinaigrette to the skillet. Toss until all the ingredients are coated, adding the reserve pasta water, if needed, to loosen the pasta.
Transfer to a large bowl and serve.