What cracks me up about this scene in the original work is that all Aya does is swap out her hat, and that is enough to convince Kosuzu she is a tengu.
The fact is, I'm a tengu!♪
Are you surprised?
Hiiyiiii
By tengu, you mean one of those beings who charge through the sky faster than the eye can see...
What is it!?
...who control the winds enough to mow down even huge trees...