Most of the radioactivity danger from nuclear weapons and reactors relates to the byproducts of the fission process, rather than to the original fissile material.
My grandfather was a mechanic in the Enola Gay's bomber group. He mentioned that his personal bar for heat and humidity are from some of the islands they setup airfields on in the Pacific. Considering he spent a fair amount of his career following that war in LA maintaining the B52 air wings I tend to wonder why more of them aren't wearing shirts.
Most of the local people on Tinian and the other northern Mariana islands historically haven't worn shirts, male or female, although standards of dress on those islands have of course westernized somewhat since Western colonization. The climate there is very suitable for going shirtless at many times of the year.