In two small bowls, stir together the ingredients for each sauce. You can use less horseradish for a milder cocktail sauce, if you like.
Soak the shrimp in the coconut milk for 5 minutes. While they're soaking, place the brown rice flour, cornstarch, paprika, salt, and cayenne in a gallon- size ziplock bag and shake to mix. Add the wet shrimp to the bag and shake it to coat them.
In a large, heavy saucepan, heat 1 1/2 inches of oil over medium-high heat (to 350° if you're using a deep-fry thermometer). Working with a third of the shrimp at a time, fry them until golden brown, 2 to 3 minutes. Use a slotted spoon or wire skimmer to remove the shrimp, then drain them on paper towels in a single layer. Serve with the cocktail and tartar sauces.