Without a monitor, I expect that you will have problems configuring Knoppix for much of anything. I wouldn't trust it to work setting it up on another system and saving the configuration, as some other hardware configuration issue is likely to get you. Had you configured a system before the monitor failed, that could well work. But at this point I really would hook up another monitor.

I do use FTP to transfer files from a system if there are Windows software issues. I'll generally install an FTP server on another system, then use an FTP client in Knoppix to transfer the files. I used to use Konquror, but I understand it has vanished from 6.2. Other browsers should work, or even the command line FTP client.