I don't think you can rewire your brain. Stuttering seems to be a neurological problem with the brain wiring out of kilter. The brain gets confused when it hears its own voice and hence stuttering occurs,. That is why we stutter less when we sing or whisper or speak in unison with another person. That is also how the Edinburgh Masker and DAF (delayed Auditory Feedback) devices work. The person speaking does not hear his voice and hence stutters much less.