You have several choices as to how much of the original wiring to re-use. See my Teardown for more detail on the fan wiring. Unfortunately this device is designed to make it almost impossible to replace the fans neatly.

In every method, you will be cutting the cables leading to the fans.

You can either re-use the existing female 2-pin connector, or buy a new one. These instructions are written assuming you bought a new connector, and are wiring the fans with a new harness.

This method has the advantage that you can test the fans/harness assembly before you re-assemble the whole kazoo, fill it up with water, and then find it does not work. (...And rinse, and repeat, and rinse and repeat, in your author's case. )