The best way to transport exotic animals between countries is shipping them. You would have to make sure you have all the necessary paperwork (import / export permits). You will also have to make sure that any animal that you try to transport is not on a CITES list as well. This adds another layer of permits and would further complicate what you are trying to do. I would suggest looking for a show your interested in going to and seeing who is on the Vendor List. Then contact the vendors to see what their suggestions are. I am pretty sure what you want to do is doable, but I doubt you would simply be able to bring reptile on an International flight as carry ons.

Good luck.