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I think this subject is discussed in Unweaving the Rainbow by Richard Dawkins.

The atmosphere contains particles that bend parts of the light from the sun at different angles. Because of the type of particles, most of teh light that reaches us is of the frequency that we experience as "blue".

That isn't a proof, it's an explanation.

And we can measure that light frequency. It is within the range that is defined as blue.

The sky is not blue. Particles have no concept of color. The human eye picks up the frequency of light and therefore assigns the sky the color blue, but if there was no human eye looking at the sky, then nothing would pick up the light frequency and give it color.

Therefore it is literally, all in your mind.

And it also means that the seemingly idiotic answer that the sky is blue because one can "see it and it is" is surprisingly close.

I can in fact provide sufficient evidence that the sky is blue, especially if I state that "blue" is defined as a color which stimulates the blue sensors in ones eyes far more than the red or green ones, and if I can say that the sky does in fact do this through replicable experimentation; i.e., "hay go look, you'll see it's blue."
However, in this distinct case, I find it arbitrarily restricting that you're not allowing pictures. After all, if I want to prove the appearance of something, I personally would just take a picture.