Whisk 1/2 cup olive oil, lime zest, lime juice, 1 teaspoon pepper, Cajun seasoning, and 1/2 teaspoon salt together in a large glass or ceramic bowl. Add shrimp and toss to evenly coat. Cover the bowl with plastic wrap and marinate in the refrigerator while you prepare the sausage.

Heat 1 tablespoon oil in a large skillet over medium heat. Add sausage and cook until browned and cooked through, 8 to 10 minutes. Transfer to a paper towel-lined plate to drain, and drain and discard most of the grease from the skillet.

Bring a large pot of lightly salted water to a boil. Cook linguine at a boil until tender yet firm to the bite, about 11 minutes.

While the pasta is cooking, remove shrimp from the marinade and shake off excess. Discard the remaining marinade.

Place garlic in the same skillet used to cook the sausage. Cook garlic over medium-high heat until fragrant, about 1 minute. Add shrimp and cook until pink, 2 to 3 minutes per side. Pour wine into the pan and bring to a boil while scraping the browned bits of food off the bottom of the pan with a wooden spoon.

Add sausage, chicken stock, cumin, remaining 1 teaspoon pepper, and remaining 1/2 teaspoon salt; cook until heated through, about 5 minutes. Add drained pasta and cilantro; toss to combine. Serve immediately.