It should be taken note that when we ourselves are being taught "stand-alone" systems by our teachers and that particular curriculum, we should remember such methods for the most part.
There's no reason for your WCK curriculum to become "tainted" by another system you do. How you personally fight using your martial arts knowledge is another thing, but teaching is quite different.
Without a proper curriculum, there is nothing to teach.
It is bias to think that the art of war is just for killing people. It is not to kill people, it is to kill evil. It is a strategem to give life to many people by killing the evil of one person.
- Yagyū Munenori