We eat potatoes, skins and all. Before eating all we do is wash them in clear water with a brush. Is that enough to remove any anti-sprouting agent that may remain on the potato?
I always wash my fruits and vegetables to remove any dirt or sand. Washing and brushing the potatoes is recommended. The sprouting agent dissipates very quickly once applied, so your method of washing in water and cleaning with a brush will work fine. Here are some articles on it from the Dr. Potato blog:
(Note: one gallon of Sprout nip for 66,000 potatoes is the recommended application.)