can he sign over parental rights?
No. There's no such thing as simply "sign[ing] over parental rights." If some other man steps up and wants to adopt the child, your fiance can sign off on the adoption. Otherwise, he chose to father a child. Therefore, assuming his paternity is properly established, if the mother seeks child support, he'll be obligated to pay.
I just dont want a happy family to get broken up because of this.
What family are you talking about, and why would it "get broken up"? You told us that the mother "was apparently still married," and I assume you're saying that she was married at the time she and your fiance had sex. Are you using the word "was" to imply that she no longer is married? If she's no longer married, then there's no concern about that family being "broken up." If they are still married, I would think the DNA test results would be enough to break up the marriage, but maybe she hasn't shared those results with her husband.
She had a choice, so does he not?
He most certainly had choices. He had a choice to have vaginal sex. He had a choice to use or not use some form of birth control. He made the choice to have vaginal sex and either not use birth control or use birth control and accept the fact that no form of birth control (other than abstinence) is perfect. Once he made those choices, he had no choice about whether or not his sexual partner became pregnant (depending on your belief system, that choice was made by (a) god or random biological chance). Once she became pregnant, the law provides that the decision to terminate or not terminate the pregnancy belongs entirely to the mother. This is a matter of law that is well known to the general population.
Since you said that payment of child support is not your concern (although it should be since, once you marry him, you will also marry his problems), then there really isn't any issue. Although he can be forced to pay child support, the law will not force him to be a part of his child's life.
Of course, if the woman is still married, she can deceive her husband about the child's paternity and pretend until the child reaches the age of majority. That's up to her.