I think William Cole sounds better, but Cole William doesn't sound bad, either. And like someone else mentioned, how often do you really use his full name? I think that it will work very well no matter which way you go with it.
My SIL has a son named Caleb Aiden. From birth, he was called Aiden by all his family members. Once he started school, though, he started going by Caleb. He's almost 9 now and he responds to either name. So just a thought that once school starts, they may call him by his legal first name, even if he goes by his middle name at home.