Workers at nuclear weapons plants were federal employees, and their health records (minus personal identifiers) are publicly available. But after Dr. Tom Mancuso and Dr. Alice Stewart published a paper in 1976 stating that Hanford workers had higher-than-average cancer rates, the government withheld the records.
Lawsuits followed, and the government only relented in 1990 (after the Cold War ended).
In 2000, DOE issued a report on a series of studies of worker health, concluding that cancer rates were higher. Congress passed a law later that year allowing workers with a variety of cancers to be compensated - although the progress has been very slow since then.
Workers at nuclear power plants are different, as they work for private companies, who are under no obligation to share health records or records of exposure (all employees wear badges measuring radiation exposure each day). As a result, there has been virtually no studies on this topic.
There was one for the Calvert Cliffs plant in Maryland years ago, but it was small and inconclusive. I know of one for Canadian workers that was in a journal a few years ago, but again, that found nothing.
Truly, I don't know of anything we can do to force the release of these records.
Radiation and Public Health Project