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From my knowledge of the Apollo Program the Van Allens Belts posed very little threat to the astronauts. The Van Allen belts span about forty degrees of earth's latitude twenty degrees above and below the magnetic equator. The principle danger of the Van Allen belts is high-energy protons, which are not that difficult to shield against and the spacecraft course was plotted so that it would traversed that region of space very quickly so as to minimal exposure to radiation. The actual course of the spacecraft was three-dimensional. Each mission flew a slightly different trajectory in order to access its landing site, the orbital inclination of the translunar trajectory was always in the region of 30°. Stated another way, the geometric plane containing the translunar trajectory was inclined to the earth's equator by about 30°. A spacecraft following that trajectory would bypass all but the edges of the Van Allen belts minimising the amount of radiation an astronaut may receive. I don't think that the astronauts were exposed to enough radiation to cause cancer. Swigert's cancer was probably more earthly then heavenly.
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