Mao recognised that China was unable to defeat the UN in Korea due to their inability to control, or even deny access, to the waters surrounding the peninsula. He even went so far as to request assistance from Stalin in the form of Soviet operated submarines to be used (in a completely deniable manner) to interdict UN naval forces operating in the region. Stalin refused so as not to be drawn into the conflict but what if instead, once the cease fire had begun, the USSR provided the PLAN with significant numbers of major units?
I know that relations deteriorated significantly between the two nations but suppose Khrushchev decided to keep up appearances by transferring significant numbers of new ships he now saw as outdated and useless, i.e. Sverdlov class cruisers and maybe even the Stalingrad class battle cruisers. Khrushchev could even have arranged a barter deal for Chinese produce and labour in exchange for completing and transferring the incomplete Sverdlovs and Stalingrads, as well as more numerous destroyers, submarines and maybe missile craft, letting the Chinese think they were getting precedence over Soviet needs for the equipment but in reality the Whiley Russians were simply recouping losses on unwanted and unneeded equipment.
The irony is, while perceived as useless in a nuclear war this fleet in being would completely change the balance of power in South East Asia and the South China Sea in particular with the various bushfire wars and insurgencies taking place in the region during the late 50s through until the early 70s. Even if never used in anger the existence of a dozen large gun cruisers and three battle cruisers, and Chinas ability to crew them would likely have forced a complete reappraisal of what exactly the west could do in the region, and potentially forced a complete re-evaluation of force levels and equipment types retained and / or acquired, as well as required force levels.
Would the US have perhaps modernised and recommissioned all of the Iowas? Maybe the Alaskas too and perhaps even Hawaii, Illinois and Kentucky could have been completed to provide sufficient big gins to protect the now much more vulnerable carriers? Would the UK have pulled out East of Suez sooner, or would they have invested more in the RN to counter the threat? Perhaps Vanguard being retained in operational service for longer and spending most of her time in the waters she was originally intended to serve in. Would the RN have gotten additional carrier modernisations or perhaps the oft delayed new build carriers, perhaps the proposed new gun missile cruisers would have been built after all as the carriers would need to be escorted by ships that could see off a Sverdlov.
Would Japan have rearmed sooner and more extensively, perhaps acquiring carriers with strike aircraft needed to defend against these ships? Would it have seen South Korea spending big on their navy and building it up much sooner, would they perhaps have concentrated on submarines as a counter as they couldn't hope to make the number of cruisers.
And of course, what would Australia have needed to do to stay relevant in the region? Would they have even have bothered trying, or just redrawn a map and pretend the world stopped just north of Java?