A cost-effective treatment of scalar-relativistic effects on nuclear magnetic shieldings based on the spin-free exact-two-component theory in its one-electron variant (SFX2C-1e) is presented. The SFX2C-1e scheme gains its computational efficiency, in comparison to the four-component approach, from a focus on spin-free contributions and from the elimination of the small component. For the calculation of nuclear magnetic shieldings, the separation of spin-free and spin-dependent terms in the parent four-component theory is carried out here for the matrix representation of the Dirac equation in terms of a restricted-magnetically balanced gauge-including atomic orbital basis. The resulting spin-free four-component matrix elements required to calculate nuclear magnetic shieldings are then used to construct the corresponding SFX2C-1e Hamiltonian and its perturbed counterpart in the context of SFX2C-1e analytic derivative theory. To demonstrate the applicability of the approach, we report coupled-cluster calculations for prototypical problems such as the (17)O shieldings of transition-metal oxo complexes (MO4(2-), M = Cr, Mo, and W) and the (129)Xe shieldings of xenon fluorides (XeF2, XeF4, and XeF6).