Umm, no. Aside from certain copyright issues going on here, how do you hope to do this "the fast way" on footage that is a) heavily compressed and b) has further reduced contrast due to (simulated) atmospheric haze? Some things simply require a lot of work. At most you can hope to use Rotobrush, but given the low quality of the footage it's gonna be one hell of a ragged edges nightmare and still require conventional masks to clean up the mess. Well, whatever. It's still gonna look fake - plopping on a clear sky on some hazy mountains just isn't "real".
Mylenium said it all. There's no "fast way". If the shot is static, you'll need one fixed mask for the mountain line, then an animated mask for the elements that go past the mountain line. It will require some tedious manual masking. If you aim to get rid of the mountains as well it will be even harder.
Whenever I need to create a matte I tend to look for the easiest solution first. In most cases involving the sky you can create what is called a procedural matte using the color channels, color controls and matte tools. It's called a procedural matte because we use a procedure instead of doing it by hand. In many cases the camera is also moving in the shot so some tracking may be required.
This tutorial shows how to use Set Channels and Colorama to create a luma matte and Mocha to track camera movement.
My technique for creating a matte from the sky is a little different. Take a close look at this screenshot. It demonstrates the creation of a procedural matte from your shot in under 5 minutes. The black solid is just a garbage matte for the foreground. Pre-compose this and use it as an alpha matte for your shot and you should be good to go.
This recent post may also give you some ideas on background replacement and tracking.