You should walk as fast as you can.
The rain wets you in two different ways: by falling on your head and shoulders and by colliding with your front as you walk forward. The amount of rain that lands on your head and shoulders is directly proportional to how long you are in the rain, but the amount of rain that hits your front depends only on the density of the raindrops. Your speed has no effect on the amount of rain that hits your front, but it definitely affects the amount of rain landing on you from above. To minimize the rain dropping onto you, you should walk as fast as you can.