Hello sir, My first thought is ask that you retain the knowledge of
the Shotokan version of Tekki first regardless of what other styles
of the kata you may practice. I will address the idea
of "bunkai"(applications) and "Oyo"(close quarter fighting) in my
forthcoming book called "The Hidden Secrets of Karate-do". In the
meantime let me say that the "hand over hand" has more of
a "salutory" meaning than an aactual application. Many kata are
derived from Chinese origins of longer kata or forms and some pay
homeage to the founder or his teacher. Remember that karate kata
tend to begin with a defensive movement to reinforce the idea that
karate is for self defense and not aggression or "first attacks." If
you look at many of the Chinese kata you will see sometime
elaborate "seals" or "opening movements" out of reverance, homeage,
or a way to denote a particular school or "ryuha." I am sure I can
find a "application" for the Shotokan Tekki opening move where the
hands or ontop of each other, but sometimes the obvious is there and
we simply overlook it. (Can't see the forest for the trees) Does
this come to mind? Heehee! Some systems using the same kata will
provide their own interpetation which relates to their train of
thought or training. This is fine. Tekki has been linked to
the "Naha-Te" of Okinawa origin but further than that has some
Chinese links. I will supply the following for more info:........

The original name of the Tekki Kata is Naihanchi. It is the name for
the Kata, which was brought by master Ason from China to Okinawa.
Ason was one the most important Karateka in Naha.

The special thing at Naihanchi was that it is executed only on a
line. It was used to teach pupils fighting at smallest space. Thus
it was executed for example on narrow beams or trees, where it is not
possible to move forward or backward. The aim was also to strengthen
the stance anyway on which background you move. In addition the
masters invented many exercise forms. The stance of the Ason
Naihanchi was Naihanchi Dachi. The Ason Naihanchi consisted of over
100 movements!
Under Itosu the Kata was separated into three parts, the Naihanchi
Shodan, Nidan and Sandan. Also the essence of the Kata changed. The
stance was not any more Naihanchi Dachi, but Kiba Dachi. The emphasis
has been shifted, which changed for example the energy flow,
particularly as the Kiba Dachi became broader in the course of the
time.

In Japan the Kata was renamed to Tekki.

Funakoshi practicing
Tekki Shodan

The three Tekki Kata were the Kata, which mastered Funakoshi first.
But he needed ten years, while he daily practiced only this Kata.
Still today there are masters, who attaches particular the importance
of number of the repetitions. They have the opinion that your should
show the Kata just after approximately 10,000 repetitions.