Is it better for the female doctor who is being slandered and defamed to testify, or to remain silent, given the witness’s refusal to be involved in relaying information, and given the oath that obliged the witness to speak?

If your testimony is beneficial to the woman and not harmful to you, then you must bear witness for her, especially if there is no other witness besides you. However, if there is real harm that will befall you from testifying, then you are not obliged to answer. An example of considered harm is exposure to imprisonment or dismissal from work. As for mere fear of the wrath of the person testified against, it is not considered harm.