In medium mixing bowl, combine rice vinegar and sesame oil. Add cucumber strips, stir carefully, and let marinate for 3 to 4 hours. Remove from marinade and drain briefly.
With hand mixer or blender, whip sweet potatoes until smooth and creamy.
To prepare sushi: Lay a piece of plastic wrap on a flat surface. Place 1/2 cup of rice on plastic wrap and press out to the size of a sheet of nori. Place a sheet of nori on top of rice, and then spread 1/4 cup whipped sweet potatoes on nori; sprinkle with sesame seeds. Arrange 1/4 cup cucumber strips in center. Leaving plastic wrap in place, roll up from the outside and dampen edge to seal (rice will be on the outside of the roll). Let chill for several hours before slicing.
Slice with a damp knife into 1/2-inch-thick slices and arrange on a serving platter. Serve cold.