No...you can not use DME if staying at a non-Disney owend resort. The Swan, Dolphin and Shades of Green all fall into that catagory.
But, you can use the Mears shuttle to and from the airport. Or you can hire a car service. Mears is about $32 pp r/t, a car service will run about $100-120 r/t, plus any tip, for up to 4 people.