Any type of cable will be just as good or bad at avoiding RF pickup no matter what signal it is used for.
The frequency of the intended signal on a transmission line does not change the way it interacts with outside radiation. Therefore the amount of RFI getting into your device as a result of the cable attached is the same regardless of whether the cable carries DC, AC, or RF. (That amount should also be very small, provided that your device has a shielding metal chassis and the coaxial connector is in contact with that chassis.)
The interaction of electromagnetic waves with anything that is composed of just metal and dielectrics (including empty air) follows the superposition principle (to a very good approximation). According to this principle, you can calculate the effects of the external RF impinging on the cable separately from the cable transporting the signal inside it, and then add the results afterward. If this were not the case, then the cable would have some nonlinear element — would be functioning as a “mixer” or “detector” — which would be very bad for the integrity of any RF signal carried on the cable.
Also, incidentally, the functionality of a coaxial cable's shield is not at all dependent on the skin effect; the effect and mode of operation is the same all the way down to DC. The case where it does have trouble is at higher frequencies (microwave and up).