Since you use Knoppix on multiple machines, the best option would be to include the cheatcode xmodule=vesa in your /mnt-system/boot/syslinux/syslinux.cfg file - in the Label Knoppix section somewhere after the APPEND ramdisk_size=
Vesa driver will run well on any hardware and you will also have the 24 bit color depth that you were asking for in one of your previous posts