The stereo output of the game boy isn't balanced, so having balanced cables shouldn't matter.
I think the "1/4" cables are of better quality" argument is also bunk; if this is really an issue, you can make your own 1/8" cables to the exact specification you think your perfect game boy pro-sound cable should be.
If you want RCA Phono outputs, I've got a thing that is gonna blow your mind:
I can't believe I posted in this thread.