No you can't. If you look on the back of the case, it only has the wiimote listed as all possible controller configurations
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You can't. The Classic Controller is not compatible with World at War.
No, you can't use the GameCube controler, but you can use the classic Wii controller.
No.
No you can't on the Wii because there is no plug for your controller.
Yes. You can choose whether to use solely the wii remote (pointer-based controls), the wii remote and nunchuk, or the classic controller/ classic controller pro. Hope this is what you were looking for!