Place first 5 ingredients in a bowl and mix to combine.
Place the grated radish in several layers of paper towel and squeeze out excess water.
In a large bowl, place all vegetables and toss.
Pour 2 tablespoons of the vinaigrette into the bowl and toss to coat, reserving the remaining sauce for dipping.
Slice the shrimp in half lengthwise.
Place the rice paper wrappers, one at a time, in a bowl of warm water to soften for 20 seconds.
Place the rice paper wrapper on a cutting board or clean surface and blot with a paper towel or towel to remove some of the excess water.
Place 4 shrimp, rounded side down, on the rice paper and top with 2 tablespoons of the slaw.
Roll one side of the rice paper over the slaw into a cylinder and then fold in the sides and continue rolling into an "egg roll" shape.
Serve with dipping sauce.