I made a
wikibox on this quite recently. Basically, you'd need Britain to have a really good reason for not giving HK back to China - maybe the Gang of Four take over after Mao, or a military junta in the 80s or 90s. Then you have to justify the UK not just keeping it for themselves - perhaps a referendum or pressure from the USA. From thereon, an independent Hong Kong would probably be hugely dependent (at first) on British and American backing to hold out against China, otherwise it just goes the way of Goa or Tibet in the
early days. However, I'd say its very possible that given time, the city being such a vital lynchpin in the international economy will ultimately end up commercial suicide to take Hong Kong.
In terms of the New Territories, yeah they're technically leased but they will be probably legally attached to the new Republic anyways and if British and American forces are there en masse in the late 90s, the PLA can't do much about it. It was pretty terrible in the 90s even IOTL, but if China has gone down the drain to the extent that Britain wants to tear up the Joint Declaration, its armed forces will probably take the phrase 'paper tiger' to a whole new level. Again though, if HK is left out in the cold on independence then they really are finished.