In that case no, I've only skinned up from the tunnel. However, the summer path up the Montagne de la Côte zig zags up very steep terrain in the trees and I'd imagine it'd be well banked out with snow which it's likely to hold for a long time given its aspect. Having tried on numerous occasions to skin up snowed-up summer paths in forests around Vallorcine I'd say it'd likely be combat skinning! Give it a go and let us know...
About four years ago in April I started my ascent from the town center of Chamonix, it's sometimes called "le vrai Mont Blanc". I know a guy who's hoping to do it this year with skis.
It's a bit tricky finding a good way from Chamonix to the tunnel entrance - worth checking out in advance. My memory is that I next followed the trail up to the abandoned lift bottom station of Le Para - somewhere along the way I put on my skis.
But after that I headed off the trail toward the NE side where I was soon in mostly open snowfields with perhaps sparse trees. (This was all in the dark, since I was going to the summit in one big push, not sleeping at the Refuge -- and the full moon's light was blocked by the Dome du Gouter)
Staying on the NorthEast of the sub-ridge followed by the hiking trail makes it more likely to find continuous snow later in a hot-temperature season (hot as in like now Today).
Met the ski tracks on the normal traverse from the modern Plan d'Aiguille lift station to La Jonction. Followed the track across the Jonction, bypassed Grands Mulets hut.
Then climbed the North ridge of the Dome du Gouter. I think it's an esthetic climbing line (very recognizable from all over valley and surrounding mountains, so you can point it out to your buddies for years afterward) - and in good conditions a fine ski descent. But I was disappointed to discover that the other parties had accepted the sustained serac-fall hazard of ascending the Grands Mulets glacier, so I had to break trail most of the way up to the NE shoulder of the Dome du Gouter.
Then traversed to the Col du Dome and deposited my skis there, finished by the normal Bosses ridge.