Well Lizzie,whilst I can accept that you should want these matters of a direct relative to be correct,let me say first of all that someone born in Connahs Quay/Shotton at that time would not have been registered in the Holywell District.I'm not offering that as perhaps my considered opinion but rather that of the co-ordinator of the North Wales BMD,Dafydd Hayes who I have just spoken to about the matter.He has forgotten more than I will ever know about Genealogy!
Of course I can accept the apparent difficulties that you face,given that Charles William died in 1882 and that you have no further Census evidence to connect with the earlier birth.One vital fact perhaps you didn't give,seeing that you have the 1856 Birth Certificate is the actual place of birth which would have been given?
Regards
William Russell Jones.