I have been messing around with this, and it's not to hard to at least extract the files from the *.exe file. From there, I apologize, but I do not have the time to help futher, but hopefully someone else will, as it is simply a matter of tracing through some batch files and seeing exactly what is being done.
As far as BIOS upgrades this is one of the more sophisticated things I've seen. It checks to make sure everything is set up: active screen set to LCD, that the laptop is on AC power, you name it. Actually pretty cool.
Anyway, you will need two tools, one free and one trial.
go to www.7zip.org
and download the free 7zip archiver. I do not know if anoher archiver can handle this format, as I didn't test them. There are very few formats that 7zip cannot handle, however, and that's what I use. Feel free to try whatever you normally use first, if you want to.
go to www.winimage.com
and download WinImage. Trial software. You can download either the exe version which will actaully install it, or the zip version that does not need any installation. If you don't anticipate using it again, just get the zip version
Ok, assuming you have the BIOS file, use 7zip to extract the file. Again, I do not have time for specific howtos, if you can't figure it out repost and hopefully someone else will respond, and I may be able to come back later with more detailed instructions.
Once you have it extracted, there will be two files. The copydisk.exe file is a disk image writer. It is not needed, and can be deleted. The other file, bios.img, is an image of a floppy disk. I was clued in by it's size, of 1440K.
Open that file with WinImage, click on the \ in the left hand pane at the top to select the root of the image file, then choose extract from the Image menu. Tell WinImage where you want to put the files, and make sure the last radio button, is selected, so that the folder paths are kept.
That's it. From there, I would start by looking at the Autoexec.bat file to trace down and see exactly how the floppy disk works. It should not be too hard to adapt it to run from either a USB memory stick or hard drive.
Hope that helps,