I think most of the officiants Disney recommends are comfortable doing both religious and secular ceremonies.
I used Rev. Kevin Knox and he offered both types of ceremonies, as well as the option to "pick and choose" what you wanted to include. I think almost all the officiants do that. His wife is also a notary and can do wedding ceremonies!
I liked Rev. Kevin. He was quick to respond to questions and very easy to work with. I had customized my vows and added some personal touches. He did everything I asked and also added his own charm and humor in a couple of places.