Changing white light to blue light without filter?

Certainly. You can buy something called a diffraction grating which is a thin piece of transparent plastic containing a huge number of extremely tiny grooves in its surface. When you shine white light on the grooves, they break up the light into its constituent colors and reflect it back towards you. One of the resulting rainbow color bands will be blue, and there's your blue light.

If the sky appears blue because blue light is scattered more than other colors, then why is the light that comes through the window during the day not distinctly blue?

Because most of the light that comes through the window is not sky-scattered light. On a clear day, much more light makes it to the ground, where it is reflected by objects. This light is not distinctly blue, and the intensity is much greater than that of the sky.

To change white light (a collection of multiple frequencies) into blue light, you need to do something with a large proportion of the non-blue frequencies. Here's what I can come up with:

• frequency dependent absorption of transmitted light (filtering)
• frequency dependent reflection (structural coloration)
• frequency dependent scattering (reflection/diffraction)

The first is simple absorption which it sounds like you don't want to do.

The second is also a type of selective absorption, but the method is different. Structural coloration may be different enough from a filter for your purpose.

The third is harder unless you have a narrow source. With a narrow source you can use a prism or a diffraction grating. The narrow source means the different angle of reflection can be controlled and you only select the frequencies you want. But if your source is diffuse, you can't control the angles. Light from one direction might give you your blue light, but the same prism will take light from another direction and give you red light.

why is the light that comes through the window during the day not distinctly blue?

Are you so sure that it's not?

Color perception is a slippery concept. Our eyes and our brain are evolved to see a consistent view of the world even under changing lighting conditions. If a thing is "white" it will look white regardless of whether it is illuminated by the light of the midday Sun or, by the reddish light of the setting sun or, by the scattered blue light from the sky.

This used to be a problem when color photography was new. People would take pictures on so-called "daylight" film, and when the prints or the slides came back, they would look at photos taken by the light of the setting Sun and ask, "Why did these all come out red?" They would look at photos taken in the shadows on a cloudless day and they would ask, "Why did these all come out blue?"

Pretty soon, photographers talked about "white balance" and finding the "white point," which meant, adjusting the colors of photographs to compensate for a colored light source. In the digital age, "auto white balance" happens in the camera, and it usually does a pretty good job...

...until you try to take a photo of a beautiful sunset, and you ask, "Why are the colors all washed out?"