Inverting current flow of RGB LED
Unfortunately your out of luck. As Chris said you either need to change your RGB LEDs to compatible Common Anode or change your driver.
Alternatively you can potentially save yourself some money and use transistors, FETs or some other type of signal converter. 

This instructable shows a simple common anode to common cathode converter that would likely solve your problem. There are also discrete transistor ICs like this that might be less obtrusive.

If you go down this road you would have to drive your LEDs like you said:

Spec              | Common (V) | R (V) | G (V) | B (V
---------------------------------------------------------
Normal            | 12         | 9     | 9     | 9
Using Transistors | 0          | 3     | 3     | 3


However, The WS chip might have trouble sinking high currents, as it is only designed to source current.

Ultimately the most logical and practical solution is to change LEDs or change driver.