Here are some pics of my Wii cut with original regulator still intact. You can cut it this far without doing any serious wire relocations.
Wii mobo front view:
Wii mobo back view:
Voltage and video relocation:
Power and eject relocation (front side mobo):
Note if you want to remove the power/standby button all together and just power it on with the voltage power switch wire pin 1 and 16 together. Which will put the Wii in always on mode.
Reset and 3v bios battery relocation (back side mobo):
Note that all components you will remove in the cutting area can be removed without any problems.
I'll try to post as much information as possible the more I trim the board. By investigating the board I can tell you that I will be able to cut it very close to the size of a cut gamecube mobo but we'll see if that will work. It will involve allot of rewiring.
As for power consumption the Wii can be powered at a minimum of 10.2v. Just like the gamecube
The amp draw at 10.2v is around 1.1-1.2A and at 12v 0.9-1A.
Have any questions feel free to ask
Edit: Here's a pic of the board running.