Some pilots will take a pet in the cabin with them to send them home... just another possibility. I'll find the link and post it...
Pilots N Paws|Saving the Lives of Innocent Animals they normally work with rescues but they may be able to help.
There are also pet friendly airlines...
I realize you still need to find out if he has a shunt or not first, just brainstorming by myself...I'd like you to be able to have a choice .... even if it means having a stranger helping out...