Precise nuclear charge radii provide stringent constraints on nuclear structure and few-body nuclear calculations. Their extraction from isotope-shift measurements relies critically on an accurate evaluation of the atomic field-shift factors. In this work, we present high-precision calculations of the field-shift factors for the helium isotopes \(^{3}\) He and \(^{4}\) He, including second-order relativistic perturbative corrections. For the \(2\,^3\!S-2\,^3\!P\) transition, we achieve ppm-level accuracy and obtain field-shift factors of \(-1212.291(1)\ {{\mathrm{kHz}}/{\mathrm{fm}}^{2}}\) for \(^{3}\) He and \(-1212.455(1)\, {{\mathrm {kHz}}/{\mathrm {fm}}^{2}}\) for \(^{4}\) He. Using these improved values, we re-evaluate the difference of the squared nuclear charge radii to \(\Delta R^{2}=1.0736(21)\, {{\mathrm {fm}}^{2}}\) based on the latest electronic-helium isotope-shift measurement. The resulting value is currently limited mainly by experimental uncertainty and shows a \(2.7\sigma \) tension with the determination from muonic-helium spectroscopy. Our results provide an improved nuclear-size benchmark for helium isotopes and highlight the importance of further high-precision nuclear and atomic studies to achieve a consistent determination of nuclear charge radii across different probes.