It is the universal fantasy of the deadbeat father (and their new girlfriend) that child support obligations can be avoided by voluntarily signing away rights. If this legal result were available, our courts would be swamped with the petitions of irresponsible parents, and the taxpayers would be supporting legions more children. If the day comes that the husband in your future stable marriage wishes to adopt (and undertake the legal obligation to support) the child, the rights of the biofather can be terminated. Until then biofather will have the obligation to support the child and, if he takes action to establish it, the parental rights of appropriate custodial access.
Best wishes for a favorable outcome, and please remember to designate a best answer.
This answer is offered as a public service for general information only and may not be relied upon as legal advice.