I was a programmer that helped put together document management systems for people trying to get some compensation for the rather extensive environmental damages caused by the nuclear weapons industry and I feel a few facts are in order:
a) All nuke stuff is already privatized. It's subcontracted out or has been to players like EG&G, Dupont, and others.
b) Originally, no contractor in their right mind would touch the manhattan project. So the government indemnified them.
c) Layers of secrecy already exist within the privatized world, and unaccountability. And the military has a hand in it is as well, obviously.
Bottom line is, the result is, we got the bombs, the mess that was made is appalling, and the full story may never really be known. The moral is, it doesn't matter who does it, civilian or military, per say, as much as, what is needed is a genuine degree of openness and accountability and that is extremely hard to do when you also have to keep everything a secret. People abuse the system.