Do you have both your stick drives with you?
7-Zip has a portable version; not sure if this will work, but worth a try:
7-Zip Portable | PortableApps.com - Portable software for USB, portable and cloud drives
Put 7-Zip Portable on one stick drive. Use it to extract the ISO to your other stick drive, or perhaps you can extract the ISO to a folder on the W7 desktop and then copy those files to your stick?