I know there are many theories leading to Tsaeci's appearance (largely due to the inconsistency with the provided lore), from being full human with snake motif, to full snake recruiting human army. For a race that once controlled Tamriel for two Eras, humans sure are bad are recording down details. Personally, I like to believe that they are shapeshifters.
I'd never thought of shape shifters, cool idea. That would certainly be quite possible and help explain the inconsistency in their description.
As was mentioned earlier though The Serpent has been a sign in TES so they do obviously exist in other forms. I am going to vote we're just looking at Talos killing a serpent. Talos was Dragonborn so I would assume he's probably held very highly by the Nords, maybe we'll find out more about the specific meaning of the statue in the game in that case.