I do not understand fully your USB stick situation: has it more partitions, 1 containing the Knoppix system with ISO9660 fs (readonly, optical CD fs), and an other one that is rw (maybe FAT32) for persistence?
If so, you cannot change the ISO9660 fs since it is like this: readonly.
I recommend you to reformat the stick with GParted (for example) to FAT32 fs, and only 1 partition. Then install GRUB2 bootloader to stick (you can use SystemRescueCD). Make a boot directory in the root of the created partition. Store all your live systems here in "boot". Depending of the size of USB stick you can download and store many systems.
Download Knoppix ISO. If you have enough memory, download in /tmp directory (in memory). Extract its whole content into boot/knx/KNOPPIX_NAME directory.
Then create grub/grub.cfg file and enter in it the appropriate menuentries for Knoppix.
In the same way you can download and start other live sytems with GRUB2 from the USB stick. You can use persistence, too.
On the net you will find a lot of information about GRUB2, grub.cfg and menuentry examples for different systems. Also for Knoppix...
If you take my advice and boot Knoppix in this way, I can give you (if you need) working menuentries for Knoppix, since I use it just in this way: started with GRUB2 from internal and external drives, USB sticks.