Hi!
Assuming that you can make it from Geneva to your starting point on Sunday, you have six days of walking at your disposal. According to my experience, you should start in Les Contamines (Easy access from St-Gervais-les-Bains which can be reached by train from Geneve-Cornavin Station).
TMB walking calls for wide weather changes, be ready.
Also, accommodations are not always available starting mid September.
Search for and abide by the locals' advices before leaving for the day.
Good luck,
Jean-Marc