I'm just back from Chamonix. I did a couple of days in Portes du Soleil but I found the natural stuff in Chamonix much more enjoyable. I did most of the stuff peasnotwar suggested and a bit of exploring. The French National Survey (blue) maps and a lift timetable are all that you need. I ended up walking one section from Flegere down to Les Tines, you are better taking the Petit Balcon back towards Cham. There is a great descent from Col de Balme to Trient on one of the GR5 varients. Le Tour and Les Houches are both worth exploring.
I didn't experience any difficulties with walkers, although nearly all the tracks are technically off-limits. Stop or slow right down and say Bonjour, Merci etc and they are usually very friendly. One old woman told me off, I said sorry, and as I was riding away her friend was pointing out that I had stopped and said hello etc.