Let me quote a few lines from a catchy little tune that I like...
"First off, what's a furry?
That's an easy thing to tell--
It's an animal that happens to be human as well.
If it walks like a person and meows like a cat
You've got yourself a furry, it's as simple as that.
If it talks like a person and flies like a bird
Then it's still a furry even though it sounds absurd,
'Cause even though birds have feathers and not fur
Mammals are the commonest type of furry in the world
So the word comes from them.
Even starting with a fly
You'll end up with a furry no matter how hard you try!"
~The Furry Song (v2) by Kurrel the Raven
So you'll be a "furry" but you'll be a little less fuzzy than most of us