Ginger I'm assuming the paternity testing is voluntary IF the partner even knows about the pregnancy. I think most of us probably know of our partner's feelings about abortions or if they would be the type to refuse consent to keep us in an abusive relationship in which case who would be foolish enough to tell them we were pregnant in the first place.
It would really be about being able to get 24-48 hours for procedure and recovery. I had a cousin I played 'alibi' for when she was a teen so her parents wouldn't know she'd had a abortion. As far as her parents ever knew she and I spent a day together 'shopping' and then she spent that night at my house. She went home the next day in the early afternoon and they were none the wiser. Her parents certainly would have bullied her into marrying a boy she wasn't really in love with in order to 'save face' in the community.
OKLA also isn't that big of a state. Hopefully a woman would be able to travel to another state or a woman's group would start some kind of 'underground railroad' to help them.