Haha, I'm amazed at how much the human race can overestimate its abilities. It's a freaking planet (natural satelite, whatever.). You can't blow it to bits with a tiny missile.
And generally, we're not all that powerful and dangerous to ourselves as some like to think. Yes, the Earth is really polluted at the moment, but I bet that if the entire human race dissapeared in a single moment, it wouldn't take nature all that long to fix what we've broken. Hell, nature can actually pollute ITSELF, and has done so numerous times before we even came to be (volcanic ash and cosmic dust are forms of natural pollution, for example), and yet it's still here.
Same goes for the Moon. Only the Moon is basically a dead planet by itself, there's no atmosphere or biosphere to pollute, and even if there is water, as Spunky said, it can't actually spread that much, no matter how massive that missile is. For ****s sake, we've survived Hiroshima and Nagasaski, Chernobyl and the mother****ing Tsar Bomb (do you have any idea how big that thing was?). These went on on EARTH. This is sent to the MOON. Absolutely, ABSOLUTELY nothing to worry about.