Wouldn't a 5000mAh NiMH battery be almost as big as the Wii itself?
Depends, on eBay I have seen 62000mah batts that would be the size of half a nintendo dsi.
When you start going for things like 98000mah, then it gets big and bulky.
1) Those are mostly fakes. They're functional, but no where near that capacity in reality.(and probably fire hazards to boot)
2) Those are Li-Ion or Li-Poly most times, not the older, bulkier NiMH
I already have a 5000mah nihm, It's just about the width of a belt and the length of a DS.
What voltage is this? A 12V NiHM with that capacity should be much larger. With the Amp draw of the Wii, a buck-boost converter would probably be impractical to get a lower voltage up to the 12V it wants.