So a CEO bullied you. He threatened to have lawyers look at something, accused you of behaving poorly, and accused you of being difficult. He is being manipulative. He is trying to guilt / scare you into stopping. And it worked.
For all readers... do not be afraid of lawyers. Especially if nobody has even talked to them yet. Lawyers do not like to lose cases, so will not push a losing agenda. Yet they also must do what their client asks, so lawyers looking into a concern, or even sending nastygrams... those are meaningless actions. It only becomes meaningful if and when if their lawyers indicate they believe they really have a case, or if your own lawyer believes they have a case. Everything before that is posturing and bullying.
If I were in the same situation as OP, I'd state that my intent was positive, ask to be informed of the results of discussions with attorneys, and wish them to have a nice day. Admit no wrong, make no apologies, ignore irrelevant statements (in particular personal attacks), and just let it slide until they take a real action of some kind.
Once they do take an action, then it might be appropriate to do what they want. But seriously... stop letting people be bullies.