I dont think the normal cleaning disc thing works, the one I'm thinking you're talking about is the one with the brissles that you put the cleaning solution on and it cleans the lens, that wouldn't work with the Wii because of how the disc is inserted, the system is motorized but if you look on the front of the Wii where you insert the disc is 2 flap type things that are there to prevent things from getting in there, those would wipe off the cleaning solution as you inserted the cleaning disc, so it's pointless.

You can take the front of the Wii by removing about 4 screws (tri-wing screwdriver required about 2 quid of Ebay) then use the disc cleaner without the front on the Wii.  When I replaced my Wii's case I found loads of helpful videos on you tube there was one of someone taking the front of and changing the LED's colour.