said it is NOT wise to go to chamonix on your own, furthermore if you don't know the place. Remember that top class alpinists and freeriders engage themselves there, so don't follow tracks because it can get really ugly for you. Even the "easy" routes can be tricky there; last year i found a couloir des cosmiques so fucked up, iced, crusted, avalanched that we had problems to get down even with a guide.
So my suggestion is that you could hire a guide, or join a group if the guide is too expensive. But since you describe yourself as "middle skilled off piste skier" i don't think it'll be wise to do otherwise.
Keep also in mind that we had tons of snow last week and on the glacier snow will be pretty unstable. In addition there is another front coming, so being stucked in a shitty situation up there will be extremely dangerous