You must have been supplied a wire harness for the Vision system where the green wire is present. On the Smart Siren, there's no green wire in use. Just cut off that wire and proceed as normal.
Silent But Deadly, it is not true that the vehicle chassis is a "floating" ground. The reason for the two ground connections is due to the separate microprocessors in the system, one for the lightbar and one for the siren that needs to "see" each other. The black wire from the harness needs to be the same ground as the lightbar ground so there's a common reference point. If the ground is separate from each other at a distance, there will be a floating ground condition where the voltage difference between the two ground points exists and the two processors no longer have a reference point to work with. That's why the Vision system balks when that condition exists, thereby the need to adhere to the instructions.