Not sure if you are looking for something more 'disposable' or not but
my mom bakes cakes by the dozen for church, friends and neighbors. She starts out by getting cheap but pretty plates from Goodwill - usually for about $1. Then she gets cheap cake carriers from Dollar Tree - one hint - don't count on them being locked or strong, always carry by the base - I learned the hard way - the bottom flexed enough that it slipped out of the lid and fell - I managed to catch about 1/2 of it in the lid as it fell to the ground. Not sure what you mean by 'then on to recipient' - whether you are shipping it or what but if needed, you can pack in a box from there. If not looking for a 'disposable' solution, my square folding cooler from Costco is perfect for things like this and allows me to put some ice packs around it to keep it cool. And I have seen some shipping boxes that have a silver insualted bubble wrap liner but I don't know where to get them.