If you BIOS does not have an 'update from USB' or the manufacturer does not have a linux bios updater,
I would leave it as is.
If you absolutely MUST update because your the life of a kitten is in peril...
Apart from reinstalling Windows on same or another temporary HDD, I would check out Hasleo WinToUSB to make a Windows
USB key that boots... but this would be playing with fire IMHO. (i.e. Wrong flash = dead machine).
Cheers!