honestly I dont even like touchless car washes - they rely on some really heavy duty surfactants to lift dirt as there is no physical agitation to lift it.
That surfactant sometimes can also damage the clearcoat..
Hence I always believe in bucket + sponge + car shampoo after hosing down the loose dust and wetting the entire body too. Good shampoo actually makes water slide off hence drying is easier. Takes 15 minutes tops for a "general outside clean" job.
Using dish soap? - if that stuff can lift "charbee and grease" do you think it will leave your wax on the finish?