I wanted to try out the Wii Classic Controller for a while now, and earlier this week I was finally able to do so.
The Classic Controller is a controller that you plug directly into the Wiimote, so while it's a wired controller, it wirelessly connects to your Wii (or Wii U) by piggy-back riding on the Wiimote's wireless functionality. And yes, it's as clunky or messy as that sounds. It works well enough, but good golly dealing with wires for all these Wii addon pieces really puts a challenge on whatever controller storage situation you have going.
I chose the GameCube classic Super Mario Sunshine to try the controller out, and you'll find the video of this below. It is mostly of me playing the game, but I thought that would give you the best way of seeing how well this controller might work for you.
As I mentioned in the video, too, if you have a first-generation Wii and can sit closely enough to your television (or find those extension cords), an original GameCube controller might be a better choice, but the Classic Controller certainly works. All the buttons map correctly and as you would expect. It's only real downside are the very clunky feeling R/L triggers, and to a lesser extend, its less than ergonomic shape.
I hope this was of some use to you.