The F10 BIOS has a feature that allows users to update in qflash using a memory stick, but of course this option is not available to you at only F4. The only other way for you to flash is using @bios. I've done it without problem but many others have lost their cmos chip due to faults...your call.
To use @Bios and get the correct bios try different download mirrors as in my experience some offer you different versions. As is said above tho' its your risk and without the floppy option your going to be limited to what @Bios finds.. Can you not just attach a floppy to the mobo just for this one task?
Get a USB FDD and connect it directly (not though hub) and it should work just remember to set the boot option as USB-FDD and not FDD and first time using the disk save the old bios onto the FDD (if not room for two reboot after saving and transfer it onto another FD. (so you put the old bios on in case of diaster.