"It is possible to delegate the responsibility of looking after a child to a married or unmarried partner, child minder, teacher, friend or relative, but the person with Parental Responsibility is still liable and responsible to ensure that proper arrangements are made for the child."
childlawadvice.org.uk/information-pages/parental-responsibility/
Is the child already born? Are you married? If no to both, you could simply not name him on the birth certificate. He'd never get parental responsibility in the first place.
Otherwise I believe legally the only way to do it would be for both of you to relinquish parental responsibility and then for you to adopt your own child as a single parent - a version of step-parent adoption without the step- which is so much hassle and paperwork I highly doubt it can be done in reality.
I'm a bit confused though as to why you might want this. Why would you opt out of maintenance (or at least the chance to claim it if at any point during your child's life you so need) in return for extremely little extra control on your part? The only things you would NEED your ex's agreement for are changing the child's name, being adopted by a step-parent, moving abroad, and applying for an emergency passport (for some unknown reason, since it isn't required for a normal one). I assume he also wants no contact, so if he had an opinion on any other thing, he would get absolutely nowhere in taking you to court to try and prevent it. He presumably wouldn't be so heartless as to refuse a signature for an emergency passport in a genuine emergency. (My ex is an arse but even he agreed to that when FIL was dying). And if you did want to do one of the other three things, you could also get a court order to do them if he absolutely refused.
If you are worried about care of your child automatically going to your ex if you were to die this is also extremely unlikely if there has never been any relationship between them.