There does not appear to be a specific diet that helps or hinders those with CMT.
However, the disease is generally less limiting in those who maintain a healthy weight and are physically active.
It is commonly considered beneficial to maintain a healthy, balanced diet and a weight in the healthy BMI range, although the means by which this is pursued is not overly prescriptive.
(My personal preference is for a moderately high protein diet, as I find this gives me most energy, and helps me sustain lean muscle mass.)