That is a very specialized ribbon cable, so you wont find them unless you sacrifice another shuffle.
Your best bet is to find another that is dead for other reasons and scavenge the ribbon cable. it doesn't look too hard to replace, assuming you got the thing open, as the ribbon cable just clicks into place. iFixit has instructions and even a sales page (but they are all out of them). The $30 they were asking doesn't seem worthwhile when a new one is $70
you cant solder ribbon cable, and you cant buy any in that shape, because Apple had that one specially fabricated.
You're out of luck, as another poster said, this is just a lesson on "Fragility" for the kid.