Place shrimp in a 9x13-inch pan. Pour lime juice over shrimp so they are completely saturated and none are exposed. Refrigerate 4 hours to overnight.
Chop tomatoes, cucumbers, red onion, and cilantro into small pieces. Add to the pan with the shrimp. Peel and chop 3 oranges and add to the shrimp. Squeeze the juice of 1 orange into the mixture. Add ketchup and hot sauce and mix well. Taste, using a tortilla chip as a spoon. Season with salt, if desired.