You can copy the data over exactly how you say.
I believe what you buy from the Nintendo Shop Channel is both the license to play the game and the game itself, and that any Wii that doesn't have the license installed can't play the game, but any iteration of the game, on your card, downloaded from a friend's Wii, or even found off the internet can be played on a Wii that does have the license purchased and installed.
As far as saved games go, a lot of the time, that data is stored on the Wii, even if the game, itself, is not, so you might be in less trouble than you think.