Just came back from my first trip to Tsan Yuk. I'm 36 and 13 weeks along. I initially registered just last week at my local Maternal and Child Health Clinic (MCHC) at Tang Chi Ngong, which made the appointment for me at Tsan Yuk for the glucose test which requires two blood samples as well as the first of two scans for nuchal transluscency for Down's Sydrome. I had a 9am appointment, had my first blood sample taken, went to the scan for the nuchal transluscency test and made an appointment for the next scan at 20 weeks during the 2-hour period that I had to wait for my next blood sample to be taken. I was out of there by 11:30am. So, it looks like I'll have 2 scans in total and there was practically no waiting time - no more than when I had health insurance and went private six years back. The nurses had great English and there were lots of "foreigners" in the waiting room - counted at least 20% Caucasian faces and there were probably more Asian foreigners, like myself as well.
You'll need to first find out where you'll be living to register at the nearest MCHC which will determine at which hospital you'll deliver. They tell you that you need to bring copies of you and your husband's HKID, proof of address in Hong Kong (e.g., water/electricity/gas bill), a letter from a private doctor certifying you're pregnant and a urine sample. I didn't have the last one, but they allowed me to collect one while I was there. Hope this helps!