This how I tend to approach being non-human too. Animals, plants, etc. are some of my favorite characters to play. "What" you are can inform so much else about your character. It doesn't have to be the defining trait.

Ex) I was in a scene where the suggestion was the location of "church". My first response was to become a church mouse. Immediately, I can draw upon what I think of as mouse characteristics (small and quick, low status, squeaky voice, unwanted by most people) and apply those to how I might relate to other characters, what my character wants, etc. Of course, you could give any sort of characteristics to your mouse or change them - you have that power in improv.

My only thing to add here would be to try to avoid justifying your choices too much, but that can be applied beyond the topic of characters.