Considering the size of the Wii, the easiest solution it to just take the whole system. Especially since your friend will already have all the necessary hookups. There is a way to get your save onto a system that has never played the game, it's just a pain. You have to play the game, as to create a local save and letting the Wii know that it's ok use save files from this game. Then, quit the game, delete that save and replace it with the one from your SD card.
You'll need two memory cards if you both have the game.
So yes, I wish the SD cards acted more like memory cards rather than a backup system. There must be some kind of security hole they're worried about to treat SD this way. And by that, I mean Nintendo must be concerned about leaving a back door open to not having to pay for VC games, that's my two cents on it at least.