Mix cayenne pepper sauce, peppers, lemon juice, garlic, salt and pepper in a food processor until almost smooth. While processor is running, slowly add oil. Transfer sauce to a resealable jar or container.
Toss shrimp in a large bowl with 1/3 cup (75 mL) sauce, using hands to rub sauce under the shell and over the flesh. Let marinate for up to 30 min.
Preheat barbecue to medium-high. Grill shrimp until cooked through, turning once, 1 to 2 min. per side. Transfer to a platter and garnish with lemon and parsley. Serve immediately with remaining sauce for dipping.