If I remember correctly on Zs <=C860, the USB option is primarily intended to work with the serial-to-USB pigtail and the CD-ROM from Sharp. This merely uses the USB Mass Storage to dump data into the internal Flash memory, since those models don't have USB host capabilities. Because the C1000 does have host, you might be able to flash with a thumb drive, but there's the still the possibility that the Z is only functioning as a Mass Storage device when this option is selected.
The best bet is probably to get a 64MB SD or CF for cheap, dedicate that to ROM flashing and keep it with your Z so you always have a failsafe in case it all goes pear-shaped while you're away from a computer. Keep the thumb drive free for other data since it's usually easier to find a USB slot than a card reader, and ~50MB of ROM installer = tons of email/more than a few MP3s.
-NXK