I understand your privacy concerns. However they're more relevant to those commercial companies that offer "marketing material from 3rd parties" where you have to opt out. I know that often also means even if you tick, your wishes are ignored and you're still on the list!
However doctors don't do that. And besides your HKID card, all other details could be faked if you wish (home address, tel). Give a temporary SIM number if you're that cautious.
The high street doctors don't have any linkage to each other, so if you register with just one to ask a specific sexual question, and never return, that's an option. Or, ask them for a professional referral. All practical avenues to pursue in your quest for the truth