Answer really depends on when the airfield deems it appropriate to activate 'LVP's'. At my home base LVP's are started when either the RVR reduces below 600m or the cloud base reduces below 400' AGL (due to the tower being so high up!!). Until LVP's are in force then CAT 1 all the way, if LVP's are in force with a cloud base of 200' then I would opt for a CAT II/III approach to avoid an unwanted go-around. If in you example the 200' cloud base is truely only over the approach runway it may take a few go-arounds from CAT I for ATC to start LVP's, of course nothing to stop you asking for it as well.