It is not possible to record the C&P exam with an audio recorder.
While state law does allow for recordings in some states with one-party consent, there are many states that require consent of all parties to the recording. In Maryland law, as long as both parties are aware of the recording and consent to it, it is legal. If one is unaware it is illegal in most cases. DC is completely different. In Washington, DC, you can record whatever because it's one-party consent.
But this is Federal law, not state. There's a statute that forbids recordings or attorneys present because the exam is investigative in nature, not judicial.
One thing, though, can you have someone present in your exam? To give morale support and take notes of the proceeding? Or at least bear witness?
I've seen several cases now of women with PTSD from MST where they have requested a female examiner, been promised a female examiner, and on the day of the exam it's a male ready to review them. In one case, the female examiner that she was scheduled with was free that hour and when the veteran put up a fuss, they brought the female examiner into the room to sit by her while the male examiner conducted the exam. Then, after asking the questions in the C&P, the male examiner asked her to take a series of exams to uncover other mental issues and malingering: MMPI-2, MENT, TOMM. The TOMM exam is inexplicable because it is used to uncover malingering for Alzheimer's or other memory diseases. Why would that be used in a PTSD exam? MMPI-2 appears to be used to declare her PTSD as another personality disorder to deny the claim.