Plugged my IBM usb floppy drive into the 600E and ran the spsdin36.exe E: to write the files into the diskette.
Next step was to make an image from this diskette and make it a bootable CD so I could boot into my 600E.
Plugged the usb floppy into my main desktop running linux and did a couple of commands to make an image from the floppy and convert it into an iso cd image.
Making the floppy image:
sudo dd if=/dev/sdb of=spsdin36.img
Convert from floppy image to iso:
mkisofs -pad -b spsdin36.img -R -o spsdin36.iso spsdin36.img
I burned the iso image to a cd and booted into my Thinkpad 600E with no problems. The update process was like 20 seconds and then it asked me to reboot. Profit!