If you're not planning to enter their CAS the assistant will have nothing to write down when you phone up and I suspect it will cause all sorts of additional controller workload to write down that you're routing from A to B, remaining outside CAS, and only requiring a Basic Service.
Better to set the listening squawk and fly your planned route. That way there's no load on the controller at all if s/he sees your squawk and isn't bothered, but allows them to ask you for more info if they need to know exactly what you're up to.