Why Did Aharon, Not Moshe, Turn The Staff Into A Serpent?

In this week's Parsha, Aharon, not Moshe performs the first 3 of the 10 plagues, Blood, Frogs, and Lice.

Rashi explains that the reason for this is because Moshe owes a debt of gratitude to the Nile River (which would turn to blood and from where the frogs would appear) which sheltered his floating cradle as a baby, and to the sands of Egypt for concealing the body of the Egyptian he had killed before he ran away to Midian to escape the wrath of Pharaoh.

However, there is another miracle performed before these 3 that Aharon, not Moshe, also performs: turning his staff into a tanin (serpent, snake, some say a kind of fish) in front of Pharaoh.

Why didn't Moshe perform this miracle? He had already done it once by the episode of the burning bush, so its performance does not seem to have any sort of association with disrespect like the first 3 plagues.

The only idea that came to me was that when Moshe turned his staff into a nachash (snake), "Moses fled from before it," (Shemos 4:3). Perhaps HaShem took this into account and thus had Aharon perform the miracle this time.

The Kli Yakar is the only perush I have been able to find that comments on this particular notion. He first clarifies that the tanin is a larger, more dangerous version of a nachash. He then goes on to explain via a series of symbolic literary comparisons from various psukim in Tanach of Pharaoh and Egypt to different animals and the tanin being more powerful and able to subdue both Pharaoh and Egypt. Moshe had demonstrated already that he was a person of character who could "take on" Pharaoh, but Aharon had not as of yet. Therefore, Aharon, who was working with Moshe (and was about to perform the first 3 plagues) had to also have a display of might that showed he was also able to stand up to Pharaoh.

While I understand the Kli Yakar's explanation, I wonder if there is anyone else out there who may have a more pshat-based interpretation. If you've heard or seen anything, please post in the comments.

Have a great Shabbos!