You could try just copying the files and then making the drive bootable using syslinux. This is the standard bootloader for floppies and other FAT filesystem based devices. Instructions and downloads are at:
I never used syslinux from Windows, so I am not quite sure how it goes, but you can always reformat the drive if it gets stuffed up
P.S. Now I think about it, you may not be able to access the files in diskboot.img from Windows, in which case you are stuck. In this case I can only suggest a live CD like knoppix, with the USB drivers to let you access the flash drive and copy the image.