This is something I've wanted to know ever since hearing the songs in the Wii's Photo channel. The Photo channel, Weather channel, and Shop channel have some really nice tunes; these aren't just throwaway tracks. The music in the other channels is solid as well. This is unexpected for background tunes in a console's menus (though channels are more than just menus, but you get my point).

I was thinking perhaps Kazumi Totaka is responsible (I think it was confirmed that he did the extremely catchy Shop channel theme awhile back), but I'd like to know for sure. I emailed Nintendo about it, but I just got a standard, "That has not been announced. Be sure to check back at  Nintendo.com; if this information is ever announced, that's where it would be!" reply.

I'll have to upload some samples tomorrow for those who don't have a Wii and haven't heard the songs.

I looked around for information on this a while ago, but didn't get much affirmative. All I found was Kazumi Totaka did the Wii Shop Channel theme as you said and Toshiyuki Sudo composed Everyone Votes Channel. It's worth noting that the interview where Totaka was confirmed made it sound like his appearance was a special one and they were very honoured:

http://uk.wii.com/wii_channel/shopchannel/

Toshiyuki Sudo seems to be an employee at Nintendo Software Planning Development, the team responsible for the channels. If anything, I'd suspect the other channels were composed by him, but I'm not inclined to assume so.