I'd love to see a GC become portable, as it has the LoZ collector's edition game with OOT and MM on it. And the 3DS is just going to be a handheld N64 (Not that there is anything wrong with it).
@OP: If you need any help at all, there is this great website called
Acidmods that specializes in modding consumer electronics. They are super helpful and the community is a ton more friendly than this one.
Oh, and chances are, someone on there has probably attempted something like what you want to do.
And one last thing, there is a portable Xbox360, so don't let anyone tell you can't do it to last gen systems.
EDIT: Topic was TL;DR, I didn't notice someone posted a video link for portable N64 w/ instructions. From that video linked to another for a portable GC w/ instructions. Good luck with either.