I can't remember cause it was many years ago. I went alone with my ID and the real marriage cert and a copy of C6's ID (I think it is just a copy, but you can ask birth and death dept to confirm). He never has to come to sign.
If you divorced and a man is listed as father, then you need his written permission even if the kid goes to a trip/study tour outside HK, for fear you two will disappear and never come back. The father has parental right to keep the child in HK so he can visit the child. That is what I heard from a divorced friend. of course it is even more troublesome if you emigrate to anyother country. Can't do it without father's written permission.
But remember, if you do not have the father's name, then C6 do not have to support the bb. Do u have enough money to raise the bb alone? Who will take care of bb when u work?
Also, if C6's family is rich, C6 may not give him any money in his will as he is illegitimate and the air hostess may have other kids in future.