Written by Kevin Wald
The clues yield a sequence of words, each of which differs in its last letter from a word for a type of animal (hence the title of this puzzle, and the "In the end, does it matter?" remark in the intro):
The letters that are changed to produce the animals spell out TIGER DRAGON DIRECTO. The director of Crouching Tiger, Hidden Dragon is Ang Lee. ("I keep my head down so he can't see me" alludes to the "crouching" and "hidden.") If the last letter of ANG LEE is changed to an R, this produces yet another animal word (and supplies the missing R of DIRECTOR): ANGLER (another term for the anglerfish, in addition to being a term for fisherman), which is the solution to the puzzle.
(An additional clue to this transformation is "Will he shoot me, or is that too easy": Ang Lee, as a director, shoots things for a living, while an angler doesn't, because it would be like shooting fish in a barrel.)