I'm not arguing that you don't need strength to have haki. I do, however, believe that the inner strength or "determination" is what outwardly manifests into some sort of technique, similarly to chakra and chi.

Yes, Luffy and Zoro have expressed determination to the capacity that they have been able to immobolize, freak out, or knock out opponents with it alone (Zoro scaring the bounty hunters on shabondy, Luffy knocking out Duval's bull, etc), the same way Rayleigh and Shanks have made people faint by their determination. However, this has a very different effect when its concentrated into some sort of attack, such as the haki arrows or Rayleigh's sword.

Haki is an aura. It can flow freely from someone, or it can be concentrated. Just as someone mentioned earlier, the starfish didn't faint from Rayleigh's haki blast. This is because its something Rayleigh can project outward in a controlled manner. How could this work under your definition?