You could definitely use Hawlucha, yes.
I have another suggestion though: Noivern.
I ran into this problem too, I had Delphox and Lucario. So I decided on Noivern for my flyer.
I will say though, overlapping types isn't too bad in game. While you want to try to have type diversity, Hawlucha is undeniably still a very good flyer, even if you have a Fighting overlap.
Hope this helps! :)