Hi 1st time mummy
Glad that you find the info helpful.
I had my regular check ups at an OB in Causeway Bay (Dr Anne Fang), and the cost was around $1000 each visit. She's quite well-known and I like her a lot as she was very thorough and patient with me (as a first time mom like you, I had a lot of concerns and she always took the time to explain things which I find very important). Originally I planned to deliver my baby at St Paul's Hospital in Causeway Bay however, I decided to use public facilities in order to save money. (I had a c-section... if I went to private hospital, I would have paid $40,000 including board and Dr Fang's fees).
Public hospitals are very different from private ones. Public ones offer basic service so the check ups are really quick (5 min), no ultrasound and the OB would not have time to answer many questions. Since you are a foreigner, when you use public hospital to deliver, you would have to pay a fee more or less same (maybe a little less) than going to private ones so I would recommend you to use private facilities.
What you would pay for the delivery depends a lot on your OB. The hospital charges around $12,000 for natural delivery and a few thousand more for cesarians. However, your OB's fee would vary by the ward you use. Basically the better the ward (e.g. private), the higher your OB's fees.
There are 4 hospitals which a lot of people use:
St Paul's -
http://www.stpaul.org.hk/english/eng_index.html
Sanatorium -
http://www.hksh.com/eng/index.html
Matilda -
http://www.matilda.org/eng/services/maternity/package.php
HK Baptist (Kowloon) -
http://www.hkbh.org.hk/en/330_obst_gynae.htm
I heard Matilda is good. But maybe it would be convenient for you to use HK Baptist which is in Kowloon side, a shorter distance from Shenzhen as compared to the other 3 hospitals. If you do not have any OB in mind, perhaps you can check with the hospitals if they have any recommendation. As private hospitals often provide out-patient service, a lot of them have OB stationing in the premises.
Re nationality, geiboyi pointed out that HK nationality is only granted to chinese decendents. I'm not sure how it works but I'm pretty sure the newborn has every right to keep Malaysian nationality.
I totally feel for you. When I was pregnant, I was also hunting for new apartment, moved home (as stayed at parents' until new home is done), then I had to work with decorator to rennovate the place... everything just happened at the same time. If you can afford, I strongly suggest you to use facilities in HK so you have one less thing to worry. If for any reason you have to use facilities in China, it would not be the end of the world

I'm sure if you research a little and talk to expats in Shenzhen, you'll be able to find someone reliable.
Good luck! I love malaysian food (and malaysians) so I'm happy to help out.