Yes, I think there will still be energy corrections. First of all, there will be a dipole contribution because the magnetic field in the center of the nucleus will not necessarily be zero. Second, if we assume the statement “Imagine all electron charges stay outside that nucleus.” in the question means the electrons will never enter the nucleus (= probability for an electron to be found in the center of the nucleus is zero), the Fermi contact contribution will be zero but the Bohr-Weisskopf effect will not be zero.