The Arduino Leonardo and Arduino Micro (as well as other third-party boards, such as the Teensy and the chipKIT Lenny) can be directly programmed to emulate a keyboard. There are examples in the IDE that show how to do this.
It is possible with an Uno, but that requires replacing the firmware on the USB interface's ATMega32U4 chip with special HID firmware. This is a non-standard setup, though, and may make programming of the Arduino through the USB port impossible. So I wouldn't recommend doing that, and would instead go for a board that can directly emulate a keyboard.
There are plenty of tutorials on the web for connecting a Wii Remote with an Arduino, (including a library), so couple that with the examples in the IDE and a suitable board and you are good to go. From then on it's just a Simple Matter of Programming...