A regular efficient bus service links Chamonix directly with Geneva Airport and also stops in Geneva itself. The buses stop outside the train station in Chamonix.
Chamonix to Geneva Airport bus times from Altibus
The last buses go at around 5 pm and you need to allow plenty of time to get there as traffic can cause delays. If the times are not suitable, a transfer service can take you to Chamonix, often for a comparable price or less, and will take you directly to the door of the chalet. If you have heavy or bulky luggage like skis or a board, a transfer is almost certainly a better option.