We report high accuracy and precision measurements of the shear modulus of colloidal solids formed from monodisperse charged latex spheres contained in an aqueous electrolyte. Standard preparational techniques as well as a recently reported advanced deionization method are applied to prepare transparent, bcc-crystalline samples at precisely controlled low volume fractions Φ= 0.003 and salt concentrations $C_{\rm s}\leq2~\mu$mol l-1. The experimental parameters are found to be extremely stable if certain precautious measures are taken. At constant experimental conditions samples of different morphologies are prepared via controlled solidification and further shear processing. Their structure, texture and morphology are analysed by various static light scattering methods. A new, non destructive, time resolved static light scattering technique is used to detect the resonant torsional vibrations excited within a cylindrical sample. Shear moduli in dependence on the concentration of excess electrolyte are calculated from the resonance spectra and compared for several sample morphologies. For the first time a sufficiently high resolution is achieved to clearly discriminate between the influence of the morphology of the sample and of the experimental parameters. We discuss the possible applications of this new approach of high accuracy shear modulus measurements in colloidal crystals to a wide range of interesting experiments.