Hi @Drakmire ,
That is probably not possible. Blender’s Hotkeys are context dependent, meaning it depends on where your Mouse Pointer is. Makes sense, how would Blender Know where to put that Color you pick with the Eyedropper:

This is just how Blender works.
As a sidenote; You seem to make a distinct difference between the Color Picker and the Eyedropper.
In this Context, they are the same. The Eyedropper can also be used to pick an Object, for instance:

(another case of why using E in the Viewport wouldn’t work.)
The title of your questions suggests that the two (Color Picker and Eyedropper) are fundamentally different.