Coronal mass ejections (CMEs) directed toward Earth can modulate cosmic ray fluxes detected on the ground. We provide definitive evidence that even moderately fast CMEs produce small-scale Forbush decreases (FDs) - brief ≤ 3% cosmic ray exclusions over a day. Tracking fronted halo CMEs with coordinated solar imaging and in situ monitoring reveals timing and efficiency signatures statistically linking intensity drops with transient shock passages at ejecta fronts. The reductions originate in weak sheath scattering zones featuring elliptical cross-sections preferentially oriented edge-on to Earth. Connecting properties of these subtle effects to remote CME structure and kinematics elucidates inner heliospheric shock physics below major FDs detection thresholds (CR ≥ 3%). This reveals an entirely overlooked category of minor interplanetary perturbations by common solar eruptions insufficient to spark major storms.