Yes, you can't get around the laws of conservation of energy. If only...
You may want to consider a larger battery powered fan like this:
10" Battery powered fan They also come in a smaller 6" personal size.
I have one of the 10" fans and I love it. It moves a lot of air and is pretty quiet. In addition to the 110V AC adapter that it came with, I have a 12V DC adapter that I use in my RV. It can also be run with 8 D cells. Great to have during a power outage.
Oh, and I also have a 10ft cigarette lighter extension cord so I can use the fan outside the RV without using D cells.