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Getting rid of WiFi is pointless unless you also plan on getting rid of all mobile phones, tablets, laptops and baby monitors, etc. since they all give off just as much, if not dozens of times more radiation than WiFi.

That said if you're insistent on it, there's no "data loss" with a proper cable of any type. Flat cables will be fine, as long as you avoid the dirt cheap ones as craigy says.

You'll want STP cables though obviously if you want to avoid radiation, since cables can give off plenty of EM radiation too, especially over long distances.