Short circular holes with a mean bias flow passing through them can absorb or generate acoustic energy depending on frequency. A recently proposed semi-analytical model (Yang and Morgans, Journal of Sound and Vibration, Vol. 384, 2016 pp. 294–311) based on the Green’s function method successfully captured this acoustic absorption and generation. The model pointed to the importance of accurately capturing the path followed by the unsteady vorticity shed from the hole inlet edge. In the present work, the effect of the path of the shed vorticity on the hole acoustics is systematically studied. The above model is combined with computational fluid dynamics tools for capturing how the path of the shed vorticity varies for small modifications in the hole inlet edge shape. A chamfered edge, a rounded edge, and two elliptical edge cases are considered to show that a very small change to the shape of the hole inlet edge can give rise to significant differences in the hole acoustic response.