Singapore's rapid economic progress is due to anything but small government. If you read Lee Kuan-yew's memoirs, you'll see the lengths to which the Singaporean government went to kowtow to Western (and later, Japanese) multinationals. They rolled out the red carpet over and over, for years, before any of those companies made significant investments in Singapore.
Also, there are several reasons why generalizing the Singaporean experience to Sinosphere countries doesn't work:
1. Although Singapore has a lot of ethnic Chinese, the country is inherently multicultural and has adopted many British cultural traditions and practices.
2. The country is very small, making social control much easier than in a country the size of China.
3. Lee Kuan-yew himself has said that the Chinese government won't be able to maintain social control as the Chinese population migrates to the cities[0]. The system will have to change, and that will be very difficult.