Buy yourself as much time as possible.
Document the abuse if you can, whether through contact with Women’s Aid, GP or via the non emergency police line if ongoing - get a crime number and you can add to it. And keep your own diary/log.
If you put him on now, that means you have to go with him to register the birth at a time when you should be minimising your stress. And then he would be on the certificate with no safeguards in place. (This is all assuming you aren’t married.)
If wait for him to apply, the first step would be an initial mediation meeting as individuals, with a view to joint mediation if appropriate. One outcome is that you both attend mediation and reach a resolution.
Another outcome is that mediation is unsuccessful, or deemed unsuitable (you should only agree to do it if you feel safe in his presence and confident you can get your points across without feeling intimidated) it progresses to court.
At court, it is overwhelmingly likely he would be granted parental responsibility but the particulars could be hashed out via a child arrangements order. This can minimise the amount of control he is able to have, and if you are named as the resident parent it also means you can take child abroad for up to a month without his permission. (A Child Arrangements Order can also sometimes be agreed in mediation and then taken to a judge to sign.)
I do encourage you to seek legal advice from a solicitor with experience in handling domestic abuse. If they seem too timid, consider a second opinion. Also contact Rights of Women and Women’s Aid.
At court/mediation you could state you are not fundamentally opposed to him being added but wanted to have safeguarding discussions and a thorough framework given the history of abuse. A solicitor can give help you with the best line to take.
People who say it is not fair on the child to leave the father off the birth certificate often do not appreciate the ramifications on both mother and baby of an abuser having instant equal legal rights. As for seeing a blank where the father’s name is:
1)You can apply for a “short form” certificate which is fairly useless for most things but has the benefit of not naming either parent.
2) If you are not concealing the identity of the father from the child, I.e. they always know his name, and not blocking them from adding their father later at their own choice, I think not initially putting the father on the certificate is by far the better option in this specific type of imperfect situation.
There’s a small chance he may not bother applying - you might be surprised. It may suit him better to choose to see himself as a victim who has been blocked from his child, rather than taking initiative/effort. But if he does apply, you have meanwhile bought yourself some time and are allowing a better framework for arranging particulars before the parental responsibility is granted.
You can also re-register the birth at any time to include him, even without a court order.
Don’t expect great things from court/cafcass but it’s your best bet.
All the best, and good luck to you.