Or an internal one. Cheap on eBay. I'd feel more secure, for I had bad experience with early Usb.
Other option: make a bootable Cd by burning the image of a Dos floppy on it. But if the flashing programme wants to write on the floppy, as is probably the case, you've lost. If it tries to write on the Cd, it won't work; if it writes in the image in Ram of the Cd, you lose the written information - for instance the image of the previous firmware version.
Next option: go with your floppy and your controller to a computer that has a floppy drive.
Such a case is one of the good reasons to keep a floppy drive on a computer, even if you deactivate it most of the time.