I already think of you as a cat.
Yes. That's kind of how language works; if the words we use no longer clearly communicate the things we want to communicate, and we don't constantly want to use lots of words, we invent more specific words. It is how we get a lot of jargon terms that in everyday use often the mean the same thing, but in specific fields mean very specific and different things. Nobody demands that you call yourself "ciswoman" in everyday use, but that doesn't mean ciswomen who deal with the transgender community a lot find no use for the term.