The shape of depth-limited breaking-wave overturns is important for turbulence injection, bubble entrainment and sediment suspension. Overturning wave shape depends on a nonlinearity parameter $H/h$, where $H$ is the wave height, and $h$ is the water depth. Cross-shore wind direction (offshore/onshore) and magnitude affect laboratory shoaling wave shape and breakpoint location $X_{{bp}}$, but wind effects on overturning wave shape are largely unstudied. We perform field-scale experiments at the Surf Ranch wave basin with fixed bathymetry and $\approx 2.25$ m shoaling solitons with small height variations propagating at $C=6.7\ \mathrm {m}\ \mathrm {s}^{-1}$. Observed non-dimensional cross-wave wind $U_w$ was onshore and offshore, varying realistically ($-1.2 < U_{w}/C < 0.7$). Georectified images, a wave staff, and lidar are used to estimate $X_{{bp}}$, $H/h$, overturn area $A$ and aspect ratio for 22 waves. The non-dimensionalized $X_{{bp}}$ was inversely related to $U_{w}/C$. The non-dimensional overturn area and aspect ratio also were inversely related to $U_{w}/C$, with smaller and narrower overturns for increasing onshore wind. No overturning shape dependence on the weakly varying $H/h$ was seen. The overturning shape variation was as large as prior laboratory experiments with strong $H/h$ variations without wind. An idealized potential air flow simulation on steep shoaling soliton shape has strong surface pressure variations, potentially inducing overturning shape changes. Through wave-overturning impacts on turbulence and sediment suspension, coastal wind variations could be relevant for near-shore morphology.