I do not suggest attempting an adoption on your own.
Your wife should have gotten a copy of the order originally. If she no longer has it, ask her lawyer at the time.
The final order itself should be available, even if the other records in the case were sealed.. If not, you will need an attorney to help you recover the order.
Good luck to you and your step son.
This is an interesting issue that is different in every state. In Kentucky, for example, the person seeking the record, your wife, would be able to petition the court to obtain any documents that she needed to move forward with the adoption, including the sealed documents from a Termination of Parental Rights. When dealing with any aspect of child custody, rights to parent, adoption or any other such issue it is most important to obtain the services of an attorney who does Family Law in your Jurisdiction. This issue should be easily satisfied with a motion to the court where the termination took place.