You're almost certainly going to be miserable if you try to carry a backpack for that long. If you really don't want to have a rack, go for an uber-big saddlebag - Carradice makes some really sexy ones. If you're not cooking for yourself or camping, all you really need is bike repair/maintenance stuff (not much space or weight), whatever changes of clothes you want, and snacks and water for while you're riding. You can easily fit all that in a saddlebag.