How do I know it's CAT III???

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Sorry TR, I don't but your country's Central NOTAM office probably does, in the UK you can call and they will look it up for you.

However, I guess maybe I'm missing something here. If the runway is CATII/III approved and you have the states approval to operate to CAT II/III in their country, and if your AOC, aircraft and crews are all qualified then you you need only to revert to your CATII/III minima adjusted for the particular runways DA/RVR.

The Jepps will advise if the runway of CATII/III equipped. On the day, your crew will operate to the applicable minima considering the weather, all the Low Vis procedures requirements both crew, airborne and on the ground.

If you haven't already, I'd look up you ops manual section on approach minima (Part A or perhaps B) and read through your airlines requirements.

Good Luck with it.