Preheat the oven to 400 degrees F.
To make the sauce: Mix the mayonnaise with the ketchup and chili sauce in a bowl or food processor. Season the sauce with lemon juice, salt and pepper, Worcestershire, crab boil and grated horseradish and reserve.
To make the sandwiches: Slice the croissants in half then lightly toast them in the oven.
Meanwhile, in a large bowl, mix the crab with the mayonnaise, cream cheese, and capers. Season the mixture with Worcestershire, hot pepper sauce, crab boil, lemon juice and salt and pepper.
Spoon or pipe the crab mixture onto the croissant halves. Arrange the sandwiches on 4 plates. Drizzle with sauce and serve.