we’ve been to Les Carroz – on the road up to Flaine – for the past 3 years. This is about 40 mins from Chamonix and is way quieter. There is a range of marked routes up there. Maps from the Tourist office.
The one that looks a cracker is from the top of the cable car at Flaine, heading north (?) to Sixt, then you could head down to Samoens, and either ride back up & over to Les Carroz, or hopefully the chair would be open.