How to alter the state of a radio button in an exposed filter to "checked" based on the view URL?
You will need to use 2 contextual filters as each one takes a different argument, for example www.mysite.com/filter1/filter2.

You're confusing the difference between exposed filters and contextual filters, and their behaviour. An exposed filter is form based. As you want a radio button,  that's perfect. However, an exposed filter passes its values either via POST or GET; the only way to get these values through the URL is via the query string.