In reply to John Ww: Just booked into the Robert Blanch refuge for end July which is on my alternative Tour du Mont Blanc (where I manage to Contamines to Courmeyeur without seeing anybody except for the first two hours of this two day walk). I asked him re the situation regarding the snow conditions and he said completely snow covered and nobody doing it. That is not to say it is impossible but not knowing your level I would would suggest that you take crampons, light weight 30 metre rope and a couple of ice screws as well as avalanche transceiver.
I would be perfectly happy doing it provided I had 3-4 people of the same standard with me. But at same ti,e I would expect the trip to take 50% longer thasn planned