Driving around Chamonix, dangerous roads?

I know that I did it on my first trip to Europe with no problem. I stuck to the larger roads, A40, 41, 43, via Annecy. Our tour buses also drive these roads. If you want to try a smaller road, you could ask about conditions at the Chamonix tourist information. Even if no snow, they might have rock-slide warnings, etc.

It's perfectly ok To drive through the paved mountain roads during daytime,

If the danger relates to snow, you won't have to worry in August. I won't actually drive it until September so I'll be behind you.

As noted above, it's not going to be an issue. I'm puzzled, in fact. In fact, the fastest route through Geneve are low-land valley roads, and the main climb, I recall, is through the Jura over a toll highway. Were you planning on taking an alternative route? Even then, as noted, in August the roads will be clear and even the danger of falling rocks will be low.

Gooster, I was puzzled too at the warning on the Michelin maps, that is why I asked.

"Dangerous" probably means pay attention, be prepared to slow down for sharp curves (I think there are a couple of hairpins), maybe no shoulders. They are not especially problematic. The only proglem I recall is that the really scenic bits are on those sharp curves, hard - but necessary - not to look at the views.