The perturbation-theory study of universal conductance fluctuations is generalized to systems with electron scattering in a static random magnetic field. Our calculation confirms the intuitive expectation that the amplitude of fluctuations coincides with the universal value typical for the unitary random-scattering ensemble. An application of this result to micrometer-size wires with the two-dimensional electron liquid near filling factor ν=1/2q allows us to predict aperiodic Coulomb-type oscillations in this system beyond the Coulomb-blockade regime, which would manifest a correspondence between the Aharonov-Bohm and Aharonov-Casher effects specific to composite fermions.