Well, I would say the easiest way to get around this is to handle the color changes outside of the variant system, since this is a very easy thing to keybind.
However, if you need to do this within the Variant Manager system, I would recommend looking into the way the default Variant Manager project does this.
The Bosy mesh is decoupled from the actual componenet, so it can be switched out to other meshes as needed. Then, for the body color, it calls the color change for the switchable mesh, instead of for the individual components.
