There's two possible interpretations here. The implication of "shadows travel faster than light" is that information about the lack of light is faster. This interpretation is false. In your thought experiment, the information of the lasers moving still only travels at speed of light, even if the actual movement took only a fraction of that time. So the "shadow" on Earth reacts at the speed of light to changes in the source.

However, if the idea is that a laser that is continuously lit can "sweep" a path, such that the laser dot appears to move faster than light could travel that same path... Then of course that's trivially true. The light is traveling the radius of the arc, not the length.