My daughter was in breech and my private doctor said he was not qualified to do an ECV. He was supportive of the idea of me doing an ECV though. Fortunately I was already registered at the public hospital. He wrote me a letter attesting to the fact that my baby was in breech and recommended that they assist me with an ECV. Although my appointment was scheduled for a week or so away (and it's usually very hard to change appointments in the public system), when they saw that letter, they gave me an appointment right away and explained the options to me - ECV, C-sec or a breech vaginal birth (the last one both they and my doctor did not recommend, nor was I personally keen on trying).
So, if you cannot find anyone in the private system, you can register at the public system if you're an HKID holder (no need to be permanent resident). They bring in experts to do the ECV.
I did not end up having an ECV. I was conflicted to the last, and then on the very day my ECV was scheduled, I started contractions, so I had an emergency c-sec. I was relieved that I did not have to make the choice.