I assume that both of you want a lifelong relationship with baby?
I'm only asking because that would affect my decision. If the father didn't want to be involved with the child at all, then sorry pal, no birth privileges, no dropping in and out of baby's life as it suits you. That's protecting me and protecting a vulnerable child who needs to be able to count on dad.
But if he's planning to be a full-time dad, even with your separation, then let him start his relationship with baby at the beginning. That doesn't mean he has to be there for the whole labour. He could come in quietly (and on your terms) just for the actual delivery.
Thinking about it from baby's point of view, it's important that the child knows that no matter how things are between you and dad that you both love him fiercely, and that you will both always be there for him. And that it started right at his birth.