He could press the issue. He would have to pay for any blood testing though and that is enough to deter the average man. Especially the deadbeat ones!
I would suggest not even telling the ex he is a possibility. If he already knows (or may suspect) just do not press the subject.
Besides, if he does try anything stupid tell him flat out if he is found to be the father he WILL be paying child support whether you have a husband or not. That would probably scare him off.