Generally a car wash will induce marring into the paint yes. Theres one here that I've used several times for the same reason thats not bad, they do extensive spraying before the cars enter the wash (this is key, the wash mechanisms pick up salt and sand and drag it on all the other cars that go through the wash) and they use microfiber towels to wipe the cars down (this is AlSO key, often most of the swirling comes from the wipedown with nasty, dirty towels afterwards.
That wash costs $35 a wash though.
The better approach is to hire a professional detailer with references to hand wash it for you.
IMHO touchless washes are almost as bad as normal carwashes. For one they never get the car completely clean, for another they use extremely harsh chemicals that strip any wax from the surface and age all the plastic and seals.