If I understand: you can mount your USB drive from Knoppix and you have mandrake10 installed somewhere on your internal drive. Well a thing that you can try (it's not very nice, but it should work
): copy your mandrake installation to the USB drive (each directory except /dev and /proc which are specific). Then you just need to reconfigure some settings (like /etc/fstab file).
The problem is that, mandrake10 need to have USB disk drivers to boot from it and you must have a computer which can boot on USB device...
Sorry, If I'm a bit confused but I'm hurry