If I understand military law correctly, claiming that you are indeed a conscientious objector, and being able to prove it to a Court of Appeals, would either exempt you from service, or would place you in a non-combat department, such as the band or as some sort of civil service clerk and the like.
If that is truly the case, I would most certainly go that route. I hate the notion of violence and feel that war is ultimately pointless, usually it ends up in the obliteration of one society or surrender, after thousands, even millions of people have been killed.