While permission will be hell to obtain (unless you have deep pocket, I guess), the radiation will most likely spare your stock. GThe radiation from the gamma rays (the only one that can penetrate through the metal magazine of your film) is long gone. You don't have to worry about the stock and you'll be relativelly safe provided that you don't sleep with days at that place... Currently, you'll get more radiation if you spend a month on a aircraft carrier, pass 100 times through an x-ray machine in the airports, or get 40 x-ray pictures taken in the hospital than to shoot for a several days there. Another question is how you'll manage to convince you crew and actors to join :D
Actually, alpha-particles can be stopped by a sheet of paper or your skin. As long as you won't ingest an alpha-emmiting source you are OK.