Thaw shrimp, if frozen. Peel and devein shrimp. Place a steel blade in food processor. Add shrimp, half at a time. Cover and process with 10 on/off turns or until mixture is lumpy. Set aside. Repeat with remaining shrimp.
In a medium bowl, combine egg, soft bread crumbs, onion, sweet pepper, whipping cream, chile sauce, parsley, chives, dill, sage, salt, thyme and cayenne pepper. Stir in shrimp.
In a shallow plate, combine dry bread crumbs and cornmeal. Drop shrimp mixture by rounded tablespoons into crumbs. Using 2 forks, turn to coat shrimp mixture with crumb mixture. Shape gently with your hands to form 2-inch patties, about 1/2-inch thick. Arrange on waxed paper-lined baking sheets. Cover and chill at least 1 hour or up to 24 hours.
Just before serving, in large nonstick skillet, heat oil and butter over medium heat. Add shrimp cakes in batches and cook about 3 minutes per side or until golden brown. (Add more oil and butter as needed.) Drain shrimp cakes on paper towels. Transfer to a baking sheet and keep cakes warm in a 300°F oven while preparing the remaining cakes. Serve with Horseradish-Chile Mayonnaise.
To make ahead, prepare and cook the shrimp cakes as directed. Wrap and chill for up to 24 hours. Reheat in 375° oven about 10 minutes.
In a small bowl, combine mayonnaise, horseradish, lime juice, chile sauce and Oriental hot chile sauce. Cover and chill until serving time. Makes about 1 cup.