I've been using the public health system (specialist skin clinics) for the last couple of years. It's a thorough, if somewhat slow process, but if my skin spot is deemed to perhaps be cancerous the specialist will either cut the whole thing out, or first do a small biopsy to have it checked for skin cancer. The visit only costs me HK $65(if you have HK Id), and they'll have me back regularly to check for any other spots that might be developing.
I've had 2 cut out in the time I've been attending, so know how it works, and for me, it's a great service for the cost involved.
I'm not about to fly to Thailand when I can catch a bus to Yau Ma Tei.
Obviously it's not classified as cosmetic surgery...I'm worried about skin cancer on fair Caucasian skin and years of over exposure on Sydney beaches.
If your need is for appearances, then my skin clinic mightn't be for your needs. Hong Kong is full of cosmetic surgeons who charge through the roof for a good job. I know. I've paid the bill for my wife to have work done, and can recommend the guy she used if you want contact details. His English is very good, and the work he's done in several rounds of cutting up my wife's face has satisfied her.
I also have details of a Guangzhou specialist, which only involves the train trip for an hour, he's cheaper than hk, but still pricey, and comes recommended.
No idea about Thai clinics, and I've read that. a popular choice these days is South Korea .
Anyway, good luck, and pm me if you'd like any more information.