Pro-tip: Radioactive fallout is minimal except in the case of a groundburst detonation or a radiological device. After a nuclear detonation due to the heat you have a lot of evaporated moisture in the atmosphere which condenses as it cools taking with it most of the radioactive particulate, this results in a phenomenon know by the Hiroshima and Nagasaki survivors as 'black rain'. In other words the fallout is collected into the water and due to radioactive materials being significantly denser than water they stay where they fall or are washed away. In fact the largest collection of uranium is found in, guess where? The Oceans. Then you have to account for the half-life of an individual particle. If physics operated the way you thought it did Hiroshima and Nagasaki would still be glowing like the sun, whereas in reality the radiation levels had fallen back down to below the background radiation level (IE the level of radiation that occurs naturally) by the late fifties.
Cancer rates are higher today because we live significantly longer and are exposed to radiation levels and toxins for far longer than our predecessors were. It has nothing to do with nuclear testing except in very specific cases.