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Tubes are pretty damned stretchy, and they'll form around the cooler nice and snug. If it's an especially large cooler, you may need an extra set of hands to stretch it around, or a larger tube, but once inflated, it won't go anywhere. It helps to use a tube that's been inflated and stretched a bit first, a brand new tube will be tougher to stretch out manually.

EDIT: These things exist, too. You could cut the floor out potentially. Or this thing might work if you want to leave your cooler at home.

What river and what temp?

I typically like closed toed shoes for on the water, as I have smashed against too many rocks / things on the boat using open toed shoes. If its winter boating, I will go with a wetsuit bootie, otherwise I use something like this.

If you are only going for nine days, and not ever going to wear them again, you can get something that has a sole and toe protection for a lot cheaper.