Ludo
There is no telling what that un-connected green wire was or should be used for. It could be have been an AC Grounding Conductor - a conductor, not normally carrying current, used to connect the metallic non-current carrying parts of AC electrical equipment to the AC grounding bus, engine negative terminal or its bus, and to the source ground.  It could have been a DC Grounded Conductor - a current carrying conductor connected to the side of the power source that is intentionally maintained at boat ground potential. It could also have been a DC Grounding Conductor - a normally non-current carrying conductor used to connect metallic non-current carrying parts of direct current devices to the engine negative terminal, or its bus.
This is how I would approach it. If you have a large (typically) black wire connected to the ground buss bar at the electrical distribution panel and going to your engine, then I would remove the green wire. If you look closely at that green wire you can see it has suffered some major damage to the shielding probably from not being secured and rubbing on the prop shaft or coupling.
David