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Since you are married, the law presumes that your husband is the child's father, and the hospital will use your husband on the birth certificate. The only way to get around this would be to apply for support services and get a DNA test from the biological father. The agency will issue an administrative order that the bio-dad is not your husband and the birth certificate can then be changed via that order.
Alternatively, you can hire a lawyer or seek legal aid, and start your divorce, and the court will order the paternity test.
Hope this helps.
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I don't believe that an affidavit from your husband is worth anything, because if that was all that was required to avoid responsibility for a child, then every putative father would sign one and avoid legal liability.
The bio-dad can sign an acknolwedgement of paternity, but the Vital Statistics Office will not record him as the legal parent until a court or administrative agency issues an order to make the change.
I understand what you're trying to do, but as a practical matter, unless the hospital is willing to put the bio-dad's name on the certifcate, then it won't matter, because that's what will be transmitted to the vital statistics office.
That said, my original answer stands unchanged.
If the goal is to fix the birth certificate, then you can download and fill out the application for child support services found on this webpage, and then mail it in or have it hand delivered after the child is born.
If the goal is to file for divorce, then you will need all of your and your husband's financial records since the date of marriage, including a current statement of your husband's military pension benefits. Also, copies of vehicle or home title, and/or any receipts or evidence of ownership of other property that has no title certificate.