I recommend doing it, and it is not too difficult.
1. Get a blank floppy and right-click on it in Windows Explorer. Select Format and click the check box to create a bootable floppy.
2. Download the BIOS file (record the name of the file, you will need it later).
3. Download the BIOS flash utility.
4. Place both on a second formatted floppy disk (you can stick them on the same floppy as 1. but I recommend a different one so that you have separate disk w/just the BIOS files).
5. Reboot your computer and hit Del to get into the BIOS.
6. Set the boot order so that Removable Disk is first.
7. Save and exit the BIOS.
8. Insert the bootable floppy from 1. and let the computer boot up from it. It will stop with a DOS prompt.
9. Take out the floppy and put the other one (w/BIOS files) in.
10. Type awdflash.exe to run the BIOS flashing program.
11. If you want to save the current BIOS you can give it a name and it will save it to the floppy.
12. Type the name of the BIOS file (including file extension) on the floppy when asked to write the new BIOS to the chip.
13. Let it do its thing but DO NOT RESET while it is going through its process.
14. When asked to reset do so.
15. Go back into BIOS and change your boot order back to what you had before.
16. Save and exit BIOS.
17. You're done. Congrats.
Alternatively if you want the quick and simple way:
1. Download the BIOS file and BIOS utility just as before and stick them on a formatted floppy.
2. Reboot and during the inital boot screen (the one that shows the processor speed, memory, etc.) hit F2 and it should automatically do everything for you.
EDIT: I think there might be a way to do it from Windows as well but I don't recommend doing it this way.