The cot seat will likely be too small (it was too small for our baby when he was 5 months old). Even then, it's the best option on the plane and it's where we say this past summer. There's a trip report in my signature that gives more details also. For the majority of the flights, our baby slept either on my wife or on me, buckled in with the seat belt. We also used a baby carrier/papous for part of the flight and we found this much easier to get around the airport than using a buggy/stroller.

No need to apologize about flying with your baby in CW. As long as you stay calm your baby will usually reflect your mood as I'm sure you know. The main thing I would be prepared for is that it's a common time for teething.

BA crew seem to be at their best when flying with a baby in CW and were very good about staggering our meal services so one of us could eat while the other watched the baby.

Good luck and enjoy your trip. Let me know if you have other questions.