If you're only carrying one snake, you can use a bin inside the cooler if you prefer...that's too heavy & bulky to carry when doing a bunch of snakes, that's all...
& they take up way too much room in ice chests to take multiple snakes as I do. I'd need a caravan to get them all there. ;)
No issue with air-flow for 5 minutes or even an hour+...remember the limited air flow when snakes are shipped by air. He'll be fine.
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YES! Do it, you'll have fun & they'll learn a LOT from you. :gj: