I'm not at all familiar with your hardware. But I don't know any reason you can't have multiple sound cards, except it may confuse the knoppix installation/configuration process.
You can get Knoppix to try using ALSA (
http://www.alsa-project.org) by giving a boot parameter 'knoppix alsa'. See the knoppix web site (
http://www.knoppix.net) for this and other 'cheat codes'. You can also specify the soundcard driver to be loaded this way.
If you can turn off the built-in sound chip in the BIOS (most desktops let you do this) knoppix would have a better chance of finding the USB device. Maybe you can look at the configuration files for the two cases and merge them somehow ???