It depends how much the op has let this man into her life. Presumably he will have met your father and other relatives?
If he or his relatives and friends know any of your relatives and friends then how exactly is the op and her baby going to " disappear"?!
The op will need the support of her family in bringing up a baby ' it takes a village' to bring up a child.
How exactly is the op going to disappear? It's not practical nor feasible given her situation and community ties.
That's a huge ask of a new mother.
Op, the posters are correct to point out your ex's parental rights should he pursue this whether or not you try to claim Child maintenance.
Unfortunately even women who have suffered DV are forced through the courts to maintain contact with the father, as by law it is seen to be the child's right to have contact with his father.
If your ex is a wealthy man and/or has his family behind him- let's not be naive here- you are going to have an enormous legal fight on your hands especially given the promises he has given you.
Forgive me but you seem extraordinarily naive op. Are you very young?