My condolences as well.
As @Broele and some other have already said, your situation right now clearly falls into the category of health-wise unfit to do the exam.
I gather from your question that you cannot predict whether you'll be sufficiently recovered to do the viva in 2 weeks.
Common wisdom would advise that right now is not a good time for you to do far-reaching important decisions, and I'd extrapolate this to mean also that it is not a good time for exams that you take very seriously.
Time frame
Since you write that your issues are caused by the abrupt hormonal changes, what does your MD say about the expected time frame? They may tell you should reschedule your viva and they should then also give you an attestation saying that.
(Remember that there are medical conditions where one oneself doesn't properly sense/realize that one shouldn't e.g. do exams)
I'd recommend to notify your advisor and/or the head of your exam committee and/or the exam office ASAP since for the examiners it is much better to know 2 weeks earlier that the exam needs to be rescheduled. Particularly if the committee has external members that need to travel.
So, tell them that health-wise, you'd not be able to do the viva now, and that you cannot expect to/predict whether you'll be sufficiently recovered by then.
If you think this is better for you*, you can of course try to negotiate/decide together with the head of the committee to give it a try and see and either do the viva as planned if you are lucky and recover faster than it looks now or postpone it last minute. This option is fine if everyone is fine with it - it is unlikely to work if you have an external examiner coming from far away.
Openly and transparently deciding to give it a try will automatically also make them aware that you have health issues that may affect your performance.
* Maybe your recovery will be faster if the pressure of the viva is not lurking in the future - regardless of whether you reach your full (when healthy) potential (=> grit teeth and over with it in order to put that additional obstacle out of the way of your recovery). Or maybe your recovery is hindered by the pressure of the closely approaching viva or potentially later by a hindsight regret that you may have done better in the viva had it been postponed (=> get this obstacle out of the way of your recovery by canceling it for now, and reschedule when you are sufficiently recovered). Or ...
Only you can judge for yourself which way to go. But both options are fine in general.
Not oversharing
Usually, I'm personally very much on the side of not sharing medical details since making this the default ensures a practice that protects those who need this privacy.
So I hope for you that you do not feel pressure to explain or even justify yourself any further.
However, in case you do feel pressure, defend yourself - and that includes the possibility to reveal information that you feel less bad about revealing compared with the pressure (or e.g. danger of rumors) that you perceive. This is about your recovery, so choose what is overall best for you.
Revealing information about your situation is not a black or white choice, you can control the level of detail:
One possibility may be to reveal that you had a surgery and recovery is not as fast as one would wish for: "As you may have noticed/guessed/know, I had to have a surgery some time/2 weeks ago. Unfortunately, recovery is not as fast as I had hoped/there are complications, and I cannot predict whether I'll be sufficiently recovered for the viva in 2 weeks".
I certainly don't want to overshare or make them feel uncomfortable
You being uncomfortable with oversharing is an important feature that protects you. Be friendly to yourself and listen to your own guidance :-).
Someone else being uncomfortable with details they may hear from you is an additional protection for you. I'd say it is a 2nd line of defense that we have built-in (biologically or culturally?), in case your own do-not-share protection isn't working well, e.g. due to sickness or in case you cannot not share because illness or disability is obvious*.
Thus, their comfort is not yours to need and worry about. (And anyways, I expect your comfort with sharing should stop you earlier.)
They are professionals and have been in exams many times and thus have experience dealing professionally with life (and death :-( ) as it happens to affect exams and other aspects of professional life.
Note: if all works as professionally as expected and noiselessly, you rarely hear about this unless you are affected.
Sharing to get accomodation
* The whole question is of course far more complicated, since sharing can be prerequisite to getting help from others. People with chronic illness or disability need to dig into this and take the time to getting to a good strategy. For acute situations like yours now, giving yourself more time to recover and then hopefully doing the viva like anyone else is likely better.
(Personally I also think when a chronic disease or permanent disability is still as new as 2 weeks, it's likely too early for important long-term decisions.)