AH... another person like me....
I honestly cannot sleep without a fan..... for me it is mostly the noise... but I also like the breeze.
I found a battery operated fan at CVS two weekends ago. It uses one "D" battery.... and that works for roughly 10 hours on one battery. It was pretty strong. Unfortunately, I cannot find it on their website. You may want to drop in your nearest store.
It was about 6 inches high.... and diameter slightly larger than a "D" battery. It had a blue sleeve that was removable to insert the battery.