The choices as I see them are these, whether you're innocent or not: 1) say that you cheated, and you get to retake the test as though you never took it the first time -- you don't even fail the test! -- but you never get to ask this professor of a lecture with 600 students for a favor. 2) don't admit that you cheated, get caught in some dragnet based on pretty flawed statistical reasoning (or better yet, a witch-hunt), and "not graduate." 3) Best case scenario: You say nothing, don't get accused of anything, and you get the undying loyalty of the professor, though that loyalty fails at the first try, because it doesn't extend to you getting out of a test you by definition shouldn't have to take in the first place.
I'm a bit stunned that only 200 students "confessed."