The accuracy of V_{ud} determinations from superallowed β decays critically hinges on control over radiative corrections. Recently, substantial progress has been made on the single-nucleon, universal corrections, while nucleus-dependent effects, typically parametrized by a quantity δ_{NS}, are much less well constrained. Here, we lay out a program to evaluate this correction from effective field theory (EFT), highlighting the dominant terms as predicted by the EFT power counting. Moreover, we compare the results to a dispersive representation of δ_{NS} and show that the expected momentum scaling applies even in the case of low-lying intermediate states. Our EFT framework paves the way toward ab initio calculations of δ_{NS} and thereby addresses the dominant uncertainty in V_{ud}.