From what I know of my amateur coding for the GBA and DS. The DS API wise isn't more than two GBA merged and some extra registers(Hardware controllers) for the new functions previously missing from the GBA like mic, 3D, touchscreen and so on.
If Wii is as I suspect anyone that coded for the Game Cube would know the API from the Game Cube developement and a lot of thing would be so compatible you could literrary just copy the code you want to use from a Game Cube software.
And of course some extra functions that you would have to get aquinted to. But overall considering the rumors(Never investigated it myself) regarding how Playstation is so hard coded. That just ain't true with a modern Nintendo system. Unlike the Playstation I know that the GBA and DS Hardware handles alot of otherwise timeconsuming to code effects like blending, rotating 3D and 2D rendering and the list goes on.
What essentially is left to code is the game itself. Rather than what you generally need to code for PC and previously from what I have heard the playstation architecture where you need to code everything from rendering routines to controll implementation and th elist get big rapidly.
Nowdays though there is OpenGL and DirectX libraries for the PC. But it's still a whole lot of work if you really want to use the hardware good(Nowdays as the hardware is so fast you don't but anyway).
I'm just trying to sa,y from what I have come to known thru rumors and experience. Nintendo hardware is moneky easy to develope for.