Perhaps a video of the mentioned Araki Ryu Kata will help:
http://www.youtube.com/watch?v=n2_Z-whRDRk
Note that tori is serving tea to the uke, and as uke reaches for the tea, tori grabs uke's hand, twists it in something similar to kotegaeshi, kicks and immobilizes uke, then disarms uke by taking uke's tanto from the obi, and finally administers a coup de grace with tegatana.
I don't recall ever seeing that as part of Aikido keiko..(the tea serving part, I mean, not the kotegaeshi)