"Yes, these SPARTANS are the best soldiers we've ever created, you could throw a nuke at them and they'd simply laugh it off- wait, what are you doing with that micorwave? No, bad grunt! Put it down now!" XD So yes, I would assume that MJOLNIR is capable of handling radiation. A) It can be assumed that super-soldiers are going to be the target of such deadly strikes and B) They won't last long going EVA without protection from radiation.