Hopefully just activate ILS. There's no way you wouldn't be diverted to an airport that doesn't require a Cat III landing, even a IIIA is stupid dangerous for a trained crew. iirc you only have a 1-2 second correction window for any Cat III landing where the ILS cuts out, compared to something like 8-10 for a Cat I (which is plenty of time for an amateur that's been coached on the procedure to do a missed landing then give it back to the autopilot, that's super easy). Plus the number of airports that can even do just a Cat II at least used to be pretty low (150 in the US?), and Cat III rated airports are even fewer (I dont think there's double digits that can do a IIIB, and afaik there's still none in the world rated for IIIC...)

(edit: came off more aggro than I meant, changed wording so I sound like less of a dick!)