Kata is a preset movement routine with a preset form, so in that light I'd say that Unsoku and Tegatana Dousa are kata, but the exercises that they operate as the foundation for are not preset, since they are designed to build reactions based on the unknown. There is no "focus on empty handed kata" however as you put it. Our fundamental kata, the Randori no kata is really based on a sword but is executed using tegatana or tanto.
Thanks for the explanation.
When I said 'focus on empty handed kata', what I meant to say is that schools I've seen, and which taught a wide-range of pre-set forms, tended to do so in weapons practice (e.g. jo kata, ken suburi, etc), and not so much on movements with empty hand.
My main 'influences' have been the Ki Society and Aikikai... so it's a different and interesting way of training, always good to see how others like the Shodokan and Yoshinkan do things... after all, we are all trying to reach the same peak, just following different paths up the same mountain (or so I think)