The 300 number is simply laughable, It is not very hard to hide for such a large country like China with every tech in place, that needed to build nuclear weapons.
Actually during the last year when GlobalTimes's editorial Hu Xijin call for expand China's nuclear arsenal greatly, one key person who criticize him, Professor Yang, a top of rank government nuclear arms control expert from China, openly wrote an article criticize Hu, and guess what, one of his argument was "Just because the West claimed China has only that many nuclear warheads does not mean China do only have that many".
And besides, for a country like China, who account for about 50% of the entire world heavy industry manufacturing capacity now, its not hard to build thousands of nuclear warheads, if not more, in very short period of time (I mean, within months).
Guess what, in the cold war era, even the US, can make 6,000 nuclear bombs in a year, with 1950s era tech and 1950s era economy.