A custom live-cd...
It isn't hard to make a cd from a linux installation. If the EDK shell scrip will run under linux, you could put the shell script you refer to in the /home directory and after you have made your live-cd, run it live from a terminal or console mode(run level 3). This will run EDK as part to an OS but not put you into EFI where you want to make changes. You probably need to enter the EFI Setup as you would a BIOS, and such a live-cd won't have any effect.
From a cd, you can made a persistent USB flash of the live-cd, and be able to preserve any changes or information produced as you work.
The question is whether the script or whatever other tool you choose to use will do what you want without making any fatal mistake. I assume that EFI is like a BIOS in that if it an update fails, there is no recovery.
This is one of many Internet finds for making a live-cd.
If you need to use Windows tools, this is an example from the Internet of one way to do it with an emulator(qemu).
Here's how I did it (requires Linux knowledge) and assumes you have a USB Drive >= 64 MB.
a. boot Ubuntu 9.10 Live (or other live Linux)
b. install qemu
c. download a Windows 98 se disk image
d. create a 64 MB (empy / zeroed) file
e. load qemu with 98 se disk image as floppy and the 64 mb file as a hard drive
f. use the fdisk utility to partition and format the hard drive.
g. copy over windows 98 system files (from drive A
h. copy over the flash utility and ROM image.
i. exit qemu
j. write the 64MB file to the flash drive (eg /dev/sdz)
k. boot to the flash drive.
Is this the controller?
The utility is marked as being independent of any OS. I have read the Readme for V.17 and it states that one just runs the script from a USB drive. That is, most likely, unzip the downloaded file and put its contents on a USB flash drive; they are not the best instructions.
Why do you think you need EDK; do you have to use a text editor and flashing EFI or changing its settings isn't enough? Can you open EFI to change the settings(F2?)?
There is a V.20 with a different Readme and procedure, apparently allowing you to unzip the firmware package directly to a USB flash drive. From my experience with flashing a BIOS, the USB has to contain no other files and have any U3 utility removed. Format the USB to FAT16 or FAT32 depending on its size.
There are shell commands from Intel that might be useful in setting up EFI as you want, either as installed or while flashing it. There is a file editor among them.
Look at the Readmes for how to get into EFI and how to run the updating script. Somewhere there was a mention of F2, probably as EFI for the controller starts. It seems there should be a menu or link that will include getting to the shell and its scipt commands.
I must mention that I have never done anything like this, so do not take any irremediable action on any of my suggestions or ideas without more and better advice.