In the airline I work for, when it's the co-pilot's sector - that means from the start of the push back until the aircraft is parked.
The only parking exception is NIGS that are left seat aligned.
So with us, there is no issue with the co-pilot taxiing the airplane if the Captain is incapacitated.
I would imagine it would cost more to remove the NWS on the right side rather than leave it.