The answer is mostly, we don't know. However, we do know that most of your cells in your body are not really capable of becoming cancerous. In general (again, generalities here - we don't have enough data), only dividing tissue is really capable of becoming cancerous. But most of these dividing tissues are those mentioned above and likely to be some of the cells exposed to such a machine (immune system (not near the surface), skin, testes, breast tissue, digestive system). The tissues at the surface of your body are disproportionately susceptible to cancer.

Cancer very much is a stochastic event, and so probabilities are all we can talk about. But reducing the number of encountered objects by billions-fold while keeping the rate of exposure the same can wildly skew data that you had relied upon to determine a 'safe' dose.