That's their problem, not China's. Who says that China must use their ports to dock her future CVNs?
While I don't think this needs to be stated, but - When China intends to operate CVNs in the future, it is absolutely certain that both the PLAN and the Chinese shipbuilding industry already are fully capable of dealing with the associated complications and challenges concerning marine nuclear propulsion systems.
Furthermore, you already have USN CVNs going for port visits in pretty much every country that directly share maritime borders with China (Japan, South Korea, Philippines, Vietnam, Singapore) for decades. If they aren't concerned with the American CVNs parked inside their territorial waters right now, they wouldn't be concerned with the presence of Chinese CVNs sailing around in the region either.
If such concerns are dominant, then you wouldn't see the US building:
- 8x nuclear-powered aircraft carriers
- 7x nuclear-powered cruisers (out of the planned total of 11x), and
- More than 160x nuclear-powered submarines throughout the Cold War (and continues building more nuclear-powered ships and boats afterwards).
The same goes with the Soviet Union/Russia.
Also, since when does a conventional carrier has radioactive leak?
No. Per our sources, China is building one conventional-powered CV and one nuclear-powered CVN simultaneously right now.
(And chances are, we might (and a very big might at that) see China going for both conventional-powered and nuclear-powered carriers in the future. This is just speculation for the time being.)