I can’t hugely help with a productive answer, but this:
I know it’s a cliche, but… us blokes (at least most of us on here) want to be all rational and analytical about stuff like this. That’s not going to help here, as your wife isn’t interested in analytical explanations. About the best idea I can come up with is that she might take the advice of an authority figure she trusts – is there any such person you could get to talk to her who would explain that it’s all OK, that it’s reasonable and normal to be worried about such things, but that her concerns are unfounded?
To the power of a million – it’s not a cliche when (in this case) you can see it really is her emotions over-ruling her logical mind. It happens to all of us, and I have had many arguments with my wife, the most spectacular and quick escalating have come down to this and kids. If I ask my male friends with kids, they will agree with me. Female friends with kids, they’ll think I’m a monster and agree with her.
I’m not sure how you get around it, but just accept you’ll have to work around her emotions on this matter and show her that you care about them, rather than trying to argue logically which should (but won’t) work. If I thought it did I would suggest pointing out that visible light is EM radiation of far higher intensity than radio waves. All the harmful bands – UV, X rays, Gamma rays, are higher frequency (higher energy per photon) than visible light. But say radiation and it sounds all Chernobyl.
Good luck OP.