Do stress-induced heart attacks count?
The physical dangers of film producing are much lower than kickboxing or underwater demolitions. In fact, they're much lower than even bird-watching. On a list of "safest jobs," producing probably ranks at least as high as "the guy who writes the safest jobs list." There aren't really any major on-the-job dangers that should concern you. Barring any freak accidents with wild tigers escaping on set or low flying aircraft, you probably won't need to beef up your "accidental death and dismemberment" insurance policy much.