@Funsizefb5,
Do the paternity test but don't mail it. Bring it if she lives close enough. I'm serious. Get in the car and do it in person, either at her home or some neutral location.
If your husband is not the father, then you will retain the paternity test and please be civilized and kind about this and wish this woman well. Hopefully that will give her some closure, and if she is looking to scam you, then you will know where she lives or at least the town.
If he is the father, then it's about time he met his child.
The courts don't have to get involved until it's money time, and that is going to be a lot harder for this woman to prove (if that is her intention in contacting you, which it probably is) if the paternity test says no.