The reverse perturbation method [Phys. Rev. E 59, 4894 (1999)1063-651X10.1103/PhysRevE.59.4894] for shearing simple liquids and measuring their viscosity is extended to the Vicsek model (VM) of active particles [Phys. Rev. Lett. 75, 1226 (1995)PRLTAO0031-900710.1103/PhysRevLett.75.1226] and its metric-free version. The sheared systems exhibit a phenomenon that is similar to the skin effect of an alternating electric current: Momentum that is fed into the boundaries of a layer decays mostly exponentially toward the center of the layer. It is shown how two transport coefficients, i.e., the shear viscosity ν and the momentum amplification coefficient λ, can be obtained by fitting this decay with an analytical solution of the hydrodynamic equations for the VM. The viscosity of the VM consists of two parts, a kinetic and a collisional contribution. While analytical predictions already exist for the former, a novel expression for the collisional part is derived by an Enskog-like kinetic theory. To verify the predictions for the transport coefficients, Green-Kubo relations were evaluated and transverse current correlations were measured in independent simulations. Not too far to the transition to collective motion, we find excellent agreement between the different measurements of the transport coefficients. However, the measured values of ν and 1-λ are always slightly higher than the mean-field predictions, even at large mean free paths and at state points quite far from the threshold to collective motion, that is, far in the disordered phase. These findings seem to indicate that the mean-field assumption of molecular chaos is much less reliable in systems with velocity-alignment rules such as the VM, compared to models obeying detailed balance such as multiparticle collision dynamics.