Different models for the nonlocal description of the nuclear interaction are compared through a study of their effects on the half-lives of radioactive nuclei decaying by the emission of alpha particles. The half-lives are evaluated by considering a preformed $\ensuremath{\alpha}$ particle ($^{4}\mathrm{He}$ nucleus), which tunnels through the Coulomb barrier generated by its interaction with the daughter nucleus. An effective potential obtained from a density-dependent double-folding strong potential between the $\ensuremath{\alpha}$ and the daughter nucleus within the nonlocal framework is found to decrease the half-lives as compared to those in the absence of nonlocalities. Whereas the percentage decrease within the older Perey-Buck and S\~ao Paulo models ranges between 20 to 40% for medium to heavy nuclei, a recently proposed effective potential leads to a decrease of only 2 to 4%. In view of these results, we provide a closer examination of the approximations used in deriving the local equivalent potentials and propose that, apart from the scattering data, the $\ensuremath{\alpha}$ decay half-lives can be used as a complementary tool for constraining the nonlocality models.