Another way to put it: if the worst case happens, and a dam breaks and floods a large area, you can immediately go there and walk all over the damaged area with little more protection than a pair of sturdy boots. The worst you'd find would be things like transformer oil and some generator lubricants.
I would urge you to look at https://xkcd.com/radiation/ and compare the lines:
Living within 50 miles of a nuclear power plant for a year (0.09 µSv)
Living within 50 miles of a coal power plant for a year (0.3 µSv)
https://inis.iaea.org/collection/NCLCollectionStore/_Public/... (which concludes with "Thus, Malaysia needs to consider the possible future study of radiological impact from airborne routine discharges of coal-fired power plant.")
https://www.sciencedirect.com/science/article/abs/pii/S09698... - "Detailed studies on naturally occuring radionuclide emissions due to a 2420 MW coal-fired power plant in Malaysia."
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I'm personally much less worried about the radioactive materials from a uranium nuclear power plant than I am from coal or bad decisions on how to dispose of radioactive waste products.
We'd likely lower our radioactive footprint by completely switching from coal power to uranium.
Why are we still building coal plants then?
A nuclear plant that emitted like a coal plant would be shut down pronto.
And consider the Palo Verde nuclear plant. They had to get an NRC exemption on radioactivity of their discharge water. They had a little problem: their intake water didn't meet the discharge water requirements. They're using reclaimed sewage water--and getting the radioactivity that goes down the toilet from nuclear medicine patients.