Upvote:2
There's at least one company that offers transfers from Courmayeur into Switzerland: Knopkatransfer.com. A call to them will get you a price for a transfer to Chamonix via the Mont Blanc tunnel.
From there you can get a train (or rather, a series of trains): https://www.rome2rio.com/map/Chamonix/Zermatt
Disclaimer: this is one possible suggestion based on searches on the internet. I have no affiliations and I make no recommendations.