The School for Alexander Studies offers lessons in applying the Alexander technique to stuttering and other speech disorders. Here is an article explaining the application of the technique to stuttering.
The Alexander Technique arose out of voice difficulties. The principle behind the technique is that any specific symptom (such as stuttering) is a reflection of an overall pattern of mal-coordination or misuse. As Alexander describes it a stutterer stutters with his whole body.The process of dealing with a particular case of stuttering is written up by Alexander in his book "The Use of the Self" which is presently in print and available from many libraries or you can order it from this web-site.
The Technique deals with how people respond to the stimulus to speak, and aims to bring about a level of coordination which allows them to break the habitual response which leads to stuttering. A teacher will want to deal with the overall pattern of a person's use of themselves, before focusing in on the specific and more obvious symptoms of the stuttering.
You should understand that this is a long term reeducation process, and that you would need quite a number of lessons over a period of months rather than weeks. People often find many other benefits accrue from applying the Alexander technique, as many other symptoms as diverse as asthma, bad backs and necks and digestive problems may improve as their overall use of themselves improves.