We analyze the universal radiative correction ΔRV 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 F3(0). By connecting the needed input to existing data on neutrino and antineutrino scattering, we obtain an updated value of ΔRV=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 |Vud|=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.