I also have a GC-less Wii, and this is the adaptor that I use to connect GameCube controllers to it. (Just about any Wii-U compatible adaptor will work, even cheap clone ones like this one.) You’ll notice that this one also has two USB ports. One plug is for data, and can be plugged into your Wii. The other plug is just to provide extra power, so you can plug it into any other nearby USB socket, such as a phone charger or on the back of a TV. You may not even need the second plug if you’re only using 1-2 controllers, but I’m not sure.

Anyway, it works really well with Nintendont. Vibration works just like it used to on a real GameCube, and games that need the analog shoulder buttons (Mario Sunshine) also work flawlessly.