Hi Scott,

If you have a PC program that allows you to multi-track it should be simple enough to record the song backing from the KN 1st and then whilst playing this back lay down the vocal using your KN and USB cable as the interface for the mic.
Alternatively you can connect the mic. to the PC input using the sound card line input and a suitable mic. preamp. Results will depend to a large extent on sound card quality. Connecting a mic. directly to the sound card mic. input generally produces poor results and is not recommended.

Cheers
Len