Yep, that's correct, CAT=commercial, and from the guidance material (sect 2.3, 2nd para):
"The simplified approach is open only to non-commercial operators below the above thresholds. Commercial air transport operators are altogether excluded from the scope of the EU ETS scheme if they remain below the thresholds."
We have now heard from the EA that we're no longer on the list, so can forget about the whole thing entirely. Plus Hazel Blears and Ms Smith have gone, so it's been quite a good day, really.