You should check with an attorney, you are entitled to consultation with a JAG (usually a TDS attorney). I cannot give you legal advice on a forum, but I will give some thoughts and observations. You should get legal representation for advice you should rely on.
First, if you accept the Art. 15, there is no way that you can be denied your disability benefits. Things get a little more dicey if you demand a court-martial, but the possible level of punishments for Art. 117 do not authorize a punitive discharge, so even a conviction at Court-Martial would not strip you of your benefits (there is a chance they could then try to administratively separate you and if you are characterized with a General or Under Other than Honorable conditions, your VA benefits could be impacted. Highly unlikely, but possible).
This is what AR 635-40 has to say about the subject:
"4–1. Soldiers charged with an offense
a. Uniform Code of Military Justice action. The case of a Soldier charged with an offense under the Uniform Code of Military Justice (UCMJ) or who is under investigation for an offense chargeable under the UCMJ which could result
in dismissal or punitive discharge, may not be referred for, or continue, disability processing unless—
(1) The investigation ends without charges.
(2) The officer exercising proper court-martial jurisdiction dismisses the charges.
(3) The officer exercising proper court-martial jurisdiction refers the charge for trial to a court-martial that cannot adjudge such a sentence."
The maximum punishment at Court-Martial for violations of Art. 117, is "Maximum punishment. Confinement for 6 months and forfeiture of two-thirds pay per month for 6 months."
So, you still would not lose disability benefits under the judicial process.
As far as the elements of the offense, here they are:
"Elements.
(1) That the accused wrongfully used words or gestures toward a certain person;
(2) That the words or gestures used were provoking or reproachful; and
(3) That the person toward whom the words or gestures were used was a person subject to the code."
So, yes, the person the words or gestures were directed at need to be subject to UCMJ in order for the crime to be completed. You said the doctor was a civilian, the only potential way I could see criminal liability would be perhaps if they were a retiree or a reservist.
Generally, they cannot keep you on orders to complete a non-judicial punishment. I do not have the regulations at hand (I dealt with this issue once before when I was an Army prosecutor...that was about 5 years ago, I doubt the rule has changed, but would want to confirm that before saying for sure). But they may take your rank. If you are being separated, this could matter for your compensation, but if retired, your retired pay is based on the average of high 36 months of base pay, so there would not be a significant impact to rank reduction.
You have some big decisions to make. Either accept the Art. 15 (where you may present your defenses) or demand trial by Court-Martial. I would also consider if they would/could add additional charges if you demand the CM. This is frowned upon, but it may be an issue. You should seek the services of an attorney who can counsel you directly after reviewing your documents and represent your interests. This may be a government attorney or a civilian. I caution you again, I have not reviewed your documentation and cannot provide legal advice on the forum. I hope the insight helps you and that you get a good outcome.