We study three kinds of non-helical mean-field dynamos in a random flow with 3D shearing waves which are related to (i) shear-current dynamo; (ii) stochastic helicity dynamo; and (iii) stochastic alpha effect in the Kraichnan set-up with two independent forcing functions for small-scale random motions and alpha fluctuations in larger scales. These shear dynamos with a zero net helicity are studied for small and large magnetic Reynolds numbers while hydrodynamic Reynolds numbers are assumed to be small. In the case of large magnetic Reynolds numbers the random velocity field is considered for a small yet finite correlation time. We demonstrate that the shear-current effect and stochastic helicity effect do cause mean-field dynamos while stochastic alpha effect in the Kraichnan set-up generally do not result in a dynamo action when forcing of alpha fluctuations do not have low-frequency oscillations. We show that the shear-current dynamo requires 3D velocity field whereas stoch astic helicity dynamo can be possible even for a "quasi-2D" random velocity which has all three vector components but no spatial dependence in the direction perpendicular to the plane of large-scale shear. The stochastic helicity effect is determined by the fourth-order moment of the velocity field, while the shear-current effect is determined by the second-order moment of the velocity field. The shear non-helical dynamo represents a very generic mechanism for generating large-scale magnetic fields in a broad class of astrophysical turbulent systems with a large-scale shear, e.g., in accretion disks, irregular galaxies, stellar interiors, and in liquid-metal laboratory dynamo experiments.