In reply to higher.alpine:
While a few lucky individuals may be able to go straight up and climb a technical route on Mt Blanc du Tacul without experiencing the effects of altitude, most will feel the altitude.
The problem with altitude is that unless you've done a lot of stuff in the past you really can't tell how you will react.
Even if you've coped OK in the past, it doesn't necessary mean you'll always be OK in the future. Unfortunately the normal rules of fitness don't apply either, often the opposite!
Unless you know you're OK and live in the Alps, I'd forget doing anything technical and just get up high and see how you feel, walking with snowshoes, if OK then maybe try something more technical.
If you feel even slightly iffy or spaced, it'll be much worse when you try anything more strenuous or remotely technical.
You will not only feel under par or fluey but more importantly, your judgement, awareness and perception will be badly affected. The knock on effect will be that you are more likely to make mistakes and endanger yourself and more importantly others.
When well acclimatised I've often been with experienced but less well acclimatised folk in huts or on the hill. Chatty folk have suddenly become very quiet and they've had problems with simple tasks, such as finding and putting on harnesses and crampons and tieing simple knots or even trying to put on the right boots or do up their hoods. Unfortunately they're often not aware of their clumsiness, until I tell them and I certainly don't want them too near me when I'm climbing or setting up the belay!
If you've ever been out with a fit and active climber who's suddenly taken ill then airlifted off the Matterhorn ending up on a heart lung machine or seen fit experienced climbers killed by rocks from clumsy folk above, you'll treat altitude and acclimatisation with respect, I certainly do.
With regard to 'Chere' most folk only do the first few pitches and then ab off knocking ice onto irate folk below, so the Alpine grade doesn't really apply but boxing rules might!
If you climb Chere fully or the various Contamine routes and continue on up to Mont Blanc du Tacul, it's a lot longer and more committing. Serious in poor snow or weather conditions and much much longer. Due to the height gain you'll also feel the altitude more, which likely won't be helped by deep snow and snowshoes.
As for huts, forget the Grande Mulet's maybe think about the Torino or an alternative...
Just my thoughts
Cheers Ron