Dry ice is actually frozen carbon dioxide. I would be more worried about carbon dioxide poisoning. Remember Apollo 13? Unless you plan on keeping all the windows open and not running the AC. I once used dry ice in a cooler for a two week trip. At the end of the first week, everything was still frozen solid.
We recently took a local four day trip. The fridge wasn't working, so I froze an entire package of water bottles at home and then put them on the top racks in the fridge. By the fourth day, I still had ice in the bottles. And there was no melting ice mess like you would have with a bag of ice cubes. Just turned it into a large vertical cooler.