This concern with cancer records seems misplaced to me. There are many ways cancer is caused, not only by ionizing radiation. Some types of non ionizing radiation cause cancer, as well as chemical carcinogens, or simply genetic difficulties among others.

With the mentioned confounds alone, raw data on cancer rates wouldn't even wholly and directly correlate to the deployment of nuclear weapons. You'd need to somehow isolate from the numerous non nuclear weapon related cancer incidences and, at the very least in the case of genetic effects, it could be practically infeasible to tease out the variables in a population wide study.