I think we cannot skip the nuclear energy if we don't want to reduce the standard of living. All technologies have risk. Alternative power points like solar pannels, wind turbines can help but are not able to make enough energy, they make elecric power when the weather is adequate not when we need it and electrical network can not integrate this.
Biggest source of radioactivity is radon, izotop of radium, we get it from the rocks and soil everywhere, highest level in the buildings from brics and cement so the best you can do it is change the air in your house everyday. It's alpha radioactivity, we have been liveing with it for houndred thousend years, we tolerate it, breath in and out, but when aerosol drops stick in the lungs because of smoking or smog with this radon than we live with high risk of canser.
Old buildind industry made special risks. When the river gravel was expensive but slag of smelter was chip they made 60-80 centimeters wide ceiling from slag, and this can couse radioactivity.
Geiger-Müller instrument detect all the ionizing radiation. There are everywhere around us, from UV-B light to your mikrowave oven.