I would go for uf, but you can go for romex if there is no way rain water can get to it.
Now if your local AHJ says you need conduit, do as they say.
I was just stating that conduit is required in areas where the wire could be damaged. I have never seen uf wire run exposed before. It has to be two feet under in my area. There has to be conduit coming up to its termination. I was just curious as to where uf wire is used where it gets wet and no conduit is required (other than underground).