Toss shrimp and half the cilantro together in a bowl.
Heat olive oil in a skillet over medium heat; saute onion until translucent, 1 to 2 minutes. Add garlic and saute until browned, 1 to 2 minutes.
Stir salsa, red bell pepper, white wine, red chile pepper puree, lemon juice, and lime juice into onion mixture; bring to a boil. Reduce heat and simmer, 2 to 3 minutes. Add shrimp to salsa mixture; cook and stir until shrimp are cooked through, about 5 minutes. Garnish with remaining cilantro and add more lemon or lime juice to taste.