None that I'm aware of. Would you really want to buy disposable batteries every day on a bike tour though?

I have an Edge 800, for my use the battery has always been plenty. I also have a Garmin Fenix 3 GPS watch, and use it backpacking, which is sort of like the on foot version of bike touring, and only through the wilderness. So I've run into the same problem as far as battery power goes. I bring a smallish battery pack to charge my GPS, normally I'll top it off (back to 100%) when I set up camp.

This one costs $10, weighs 2.7 oz, and will charge my watch 7 or 8 times. I don't know what the capacity of the Edge's battery is so I can't say how many times it will charge that. This one is heavier and holds far and away more power. Assuming you run across a power outlet once a week, you should be able to find something to work for you.