"Ionizing radiation" which has enough energy to knock off electrons is the worst, as it can cause severe burns (acute) or genetic damage (cancer). But this would be up in the gamma, beta or x-ray spectrum.
At typical radio frequencies, the concern is internal heating. Cells start to die at about 107. If the blood can't carry away the heat fast enough, you could get organ damage. Microwaves would heat you so fast your organs would expand and boil, for example.
You could also get a nasty shock if you touched the equipment.
I don't know how many watts shipboard radios/radars put out, but I can see it being at least as much of a problem as it is for HAM radio operators.