Cognitive science is the most advanced understanding of the complex relation of mind and body, emotions/thoughts and behaviour/reflexes. Cognitive behaviour therapy is known the best in treating phobias – and yes, stuttering is a phobia, phobia of losing control in a speach-situation.
Even so, the therapy uses false methods, even if they succeed. We do not just think that fluency might disappear, we experience it day by day. It's reality, even if it's root is false. Programming into us that nobody gives a damn about our stutter would be a lie. Programming into us that "we can do it", recoding our social- and self-awareness: yes, that's the clue, but it's not that simple. In theory cognitive therapy misses a chain link; but in practice this chain often appears viewlessly, so the therapy works (that's why McGuire program or other therapies too might work by accident). At length, I'd recommend this therapy rather than any other. That accident could happen mostly of all there.