For the birth record itself, I'm 98% sure that you should look at the first port of call the ship made after the birth [for US births anyway; no clue how other countries handled this].
Depending on the law(s) at the time of birth and the crossing, I'm going to guess that the ship's registration played some part. For example, a US ship, Ireland-US via Canada, may have not "counted" the Canadian port for purposes of birth registration/record. I'm sure the law is quite specific but complicated by many factors [so what else is new, lol].
If you're lucky enough to locate the ship's manifest, it should show any births/deaths that took place at sea.
Someone familiar with maritime law [in the appropriate time frame] could probably answer this for you. Perhaps an email to a law library could be helpful. If you go that route, be sure to give them the date as the laws change constantly.
Best of luck. Post your findings if you get lucky!!