Yes you can get married in HK. You don't need a lawyer or any help for that, just give a Notice, and then attend marriage ceremony with your girlfriend and 2 witnesses. https://www.immd.gov.hk/eng/faq/marr...istration.html
It's not a bad idea to pay for the 2nd copy of Marriage Certificate initially.
Recognition of marriage is another question. Easiest way is if both countries signed Apostille convention. Hong Kong and India did.
So to recognize marriage in India, you just need to stamp Apostille while still in HK: https://www.judiciary.hk/en/court_se...apostille.html
To recognize marriage in other target country that didn't sign the convention(i.e. Singapore), you normally need to do full a Consular legalization, that usually involves few steps:
1) get Notarized Copy of the Marriage Certificate, if you don't have it already
2) go to target consulate (Singapore) and stamp it there.
Steps 3-4 can be done in target country, it's usually cheaper and hassle-free. But they can be done in Consulate, instead of the MFA, but that will confuse people in step 5.
3) Make translation to target country language, if necessary
4) Verify the translation+certified copy in the Ministry of Foreign Affairs.
5) Bring that copy to target country local marriage registry.
However, since you'll be applying just for the visa, the process might be much easier, so you'd better check with SG Consulate in HK for their requirements.