The sky does not skip over the green range of frequencies. The sky is green. Remove the scattered light from the Sun and the Moon and even the starlight, if you so wish, and you'll be left with something called airglow (check out the link, it's awesome, great pics, and nice explanation).
Because the link does such a good job explaining airglow, I'll skip the nitty gritty.
So you might be thinking, "Jim, you half-insane ceiling fan, everybody knows that the night sky is black!" Well, you're only half right. The night sky isn't black. The link above explains the science of it, but if that's not good enough, try to remember back to a time when you might have been out in the countryside. No bright city lights, just the night sky and trees. Now when you look at the horizon, can you see the trees? Yes, they're black silhouettes against the night sky. But how could you see black against black? The night sky isn't black. It's green thanks to airglow (or, if you're near a city, orange thanks to light pollution).
Stop, it's picture time. Here's an above the atmosphere view of the night sky from Wikipedia:
And one from the link I posted, just in case you didn't check it out:
See, don't be worried about green. The sky gets around to being green all the time.
If you were to look at the sun from the surface of the earth (I don't recommend it), it would seem yellow, but from space it's actually white. This is due to the scattering of blue light you mentioned. However, not all of the blue light is scattered, so most of it still directly reaches the earth. During sunrise and sunset, this effect is stronger, because the light has to travel further through the atmosphere, giving the air the chance to scatter more of the blue light, resulting in a more orange looking sun.
The sky looks blue because blue photons that would actually miss you are scattered in your direction, so that they reach your eyes. The intensity of this light is not strong enough to make everything look blue, especially when there is direct light from the sun, which is much brighter.
Best Answer
Not very much. When the sun is high in the sky, most would describe the light as "white", not "yellow". That would be more true for a sun low to the horizon.
The human visual system does not have a fixed mapping from input wavelengths to color perception. There are many types of "filters" in place between the two. In particular, we have an automatic "white balance" system. When you walk from a room with a single incandescent light to outside, the light hitting your clothes is very different, but you will still identify (mostly) the same colors in both places.
This system isn't foolproof, but works very well for most lighting systems you find.