Worry is unproductive in the sense of feeling anxiety, sure, but it's noble to worry at the various hammers in the archaic definition to "move, proceed, or progress by unceasing or difficult effort, to shake or pull at with the teeth."

Some of the hammers such as the hammer representing nuclear weapons - are caused by people and can be solved by people. There's a big game theoretic hill to climb over, but social pressure and advocacy have been effective at making progress. Others, like cancer and general senescence, are more of a looming threat that's a fundamental characteristic of biology, we can (and should) worry at them to make incremental progress but we're unlikely to suddenly eliminate them. The murder rate is enormously dependent on individual location and individual relationships. Traffic/bicycle/pedestrian accidents are enormously dependent on individual behavior.

Of those threats, addressing the problem of nuclear weapons - especially for a member of Nihon Hidankyo, with a personal and persuasive story of the damages these weapons caused - is probably near the top of the list for actions which can have the greatest positive change.