Strictly speaking you are correct, but what is unusual about 4 and 7 is that they usually use kunyomi even when all other numbers use onyomi (eg. ikkai, nikai, sankai, yonkai, gokai, rokkai, nanakai...). Shi/yon (4) is obviously the death taboo but shichi/nana (7) is probably mostly because it would be too easy to confuse with shi otherwise.

And yes, 9 is considered lucky in Chinese culture, but unlucky in Japan as ku ( 苦 ) can also mean "suffering". This isn't observed as much though, and in general the Japanese are a lot less keen on numerology than the Chinese...