The shadow is determined by the theme currently used by the OS. You cannot disable it for only one window. You can change the theme and turn off the shadows, but it will be a system-wide change, not related to a single window.
In your case, one of the most suitable is to create your own window structure (starting with a borderless window), which will have similar transparency properties, such as Aero. This will not be an easy task, but certainly achievable.
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