The weapon was a piece of metal but it was transformed into a key after the murder
using a key duplication trick involving a lighter and a piece of clear tape (which could be discarded or flushed or inside his wallet)
(you could also substitute a thin plastic cell phone screen protector for the tape)
it explains the sound that was created after he dumped the armor out the window,
which he only brought up because he didn't think to mention the loud sound of the armor when it went out the window
The hakama was backward because he didn't know how it was meant to be worn because he doesn't actually practice kendo.