I'm struggling to see that as a justification for a full-size carrier, especially for Hong Kong. Put bluntly, it's a bad way to do it - very expensive, and with a whole lot of capabilities that aren't related to that job. If all you're worried about is the Chinese getting at your aircraft there are ways to protect them which don't cost as much.
You're correct that the PLAN didn't have much in the way of surface ships in the mid-60s, but they did have 30-odd SSKs which are quite capable of sinking a carrier. There's also the PLAAF, and specifically their version of the Tu-16. So the escort group will need to be able to handle ASW to at least a modest level, as well as having a substantial AAW component. Really, if all thats needed is somewhere else to base aircraft, why not reclaim a bit more of the South China Sea and build another airbase? It has to be cheaper than a carrier (and escorts, and air group, and shore establishment) and it's much harder to sink.
You're also proposing a 3-way split betweek the US, UK and Hong Kong in terms of operating the ships themselves. There is certainly precedent for HK working together with the British for defence, but it does raise questions (again) about what the carrier group will be used for. Who is actually in command? If the UK is providing the bulk of the crews, they might reasonably expect to decide what the carrier group does - in which case, it's unlikely to spend all it's time stooging around Hong Kong. The RN will think that it has much better things to do with a carrier than leave it on the other side of the planet.
On the other hand , the US is providing the ships and most of the air group. There will be a lot of pressure as the 1960s wear on for the carrier to take part in the Vietnam War, which may not be to the tastes of the other nations involved.
