We analyze the universal radiative correction Δ_{R}^{V} to neutron and superallowed nuclear β decay by expressing the hadronic γW-box contribution in terms of a dispersion relation, which we identify as an integral over the first Nachtmann moment of the γW interference structure function F_{3}^{(0)}. By connecting the needed input to existing data on neutrino and antineutrino scattering, we obtain an updated value of Δ_{R}^{V}=0.02467(22), wherein the hadronic uncertainty is reduced. Assuming other standard model theoretical calculations and experimental measurements remain unchanged, we obtain an updated value of |V_{ud}|=0.97370(14), raising tension with the first row Cabibbo-Kobayashi-Maskawa unitarity constraint. We comment on ways current and future experiments can provide input to our dispersive analysis.