The lack of disc drive support isn't the only thing stopping you, there are also no controller/memory card ports for the GC on the new Wiis. It's been proven that you can install one yourself, but that can be a bit hard.
As for now, there is no way to play them on a Wii without GC ports. However, there is an app supposedly being developed called Devolution which will allow you to play GC games from USB and SD cards and will allow you to use any controller you want, but has not been released yet to my knowledge. You'll have to wait for now.