Using numerical simulations, we demonstrate that fine shape details of gold nanoring-disks are responsible for significant modifications of their localized surface plasmon properties. The numerical results are supported by optical transmission measurements and by atomic force microscopy. In particular, we found that, depending on the ring wall sharpness, the spectral shift of the ring-like localized surface plasmon resonance can be as large as few hundred nanometers. These results shed the light on the strong sensitivity of the surface plasmon properties to very small deviations of the ring and disk shapes from the ideally flat surfaces and sharp edges. This effect is particularly important for tailoring the surface plasmon properties of metallic nanostructures presenting edges and wedges for applications in bio- and chemical sensing and for enhancement of light scattering.