Mont Blanc by the Gouter route is just a high altitude slog. It's not technically difficult. I did the Gran Paradiso and then Mont B (as part of a guided 6 day alpine course) - that's the limit of my high altitude experience. As far as I know, most of the deaths on the Gouter route are when the weather closes in and people lose their way and either fall or die of exposure.
If I was you get out there and do a few routes up high over the space of a week. Try Pointe Lachenal Traverse (a great little mixed route near tacul on the other side of the Mer de Glac), Midi Plan Traverse, or if you are OK on rock, the Arete de Cosmiques.
Also Petite Verte, from the Montets cable car, would be a great starter for ten. The route up the left hand side is a PD+ but just be wary of the cornice. The normal route is, in my opinion, too easy unless it is your first ever day out after a skills course.
if you get 2-3 climbs in and feel good, have a crack at the traverse route of Mt Blanc, of course conditions and weather permitting.
However, make sure you are with someone who knows the local area and conditions/weather, it can bite if your not careful!