Verbier - Cham (or Aosta valley) would take a long time with buses and trains. First you have to go to Geneva and then down to Cham, instead of just taking a car over St Bernard (mountain pass). Verbier - Chamonix takes about 1 hour with car over St Bernard, Verbier - Geneva-Chamonix with car takes about 3 hours, with bus it probably takes forever.
Zermatt - Verbier is probably pretty easy with trains.
Make a thread on freeride.se (sedish freeski site) and see if someone is driving from Verbier to Chamonix when you're there. Lots of swedes both in Verbier and Chamonix so I don't think there will be any trouble finding someone. I live in Nendaz this winter (also 4 vallés, close to verbier), if we're heading to Chamonix at the same time you are, you could hitch a ride with us.
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