Yes; uranium and thorium are relatively common elements in the...

Yes; uranium and thorium are relatively common elements in the earth's crust; the wind naturally (and always has) picks up dust (containing those radio active elements) and blows it around the place - this has happened since (and before) the earth became habitable; nothing to do with mining and nuclear power. You also get a lot radiation from space - the sun is also a major culprit. I would suggest that your best place maybe in an unlit cave along with Sewie - problem you then have is radiation from the rocks around the cave. Do you know that you have an immune system that handles these issues, along with viruses and bacteria. Really you should concern yourself with the impact of real poisons (such as mercury, cadmium and arsenic) these accumulate. Fjordland is a granite area and will naturally have high levels of uranium and thorium; its decay of radio-active elements that produces the heat for geothermal activity for which NZ is notorious.