There are some techniques applicable to small samples that do not measure shear modulus directly, but you can obtain elastic stiffness coefficients with them and then calculate the shear modulus:
-ultrasound spectroscopy
-Brillouin spectroscopy
-Inelastic Neutron (cm samples) or X-ray (µm samples) scattering
You can measure deformations in the longitudinal directions and transversale direction.et in principal directions inclined by 45 ° using gauges. Then with the help of mohr circle Relations on deformations and of the stresses you can estimate the shear modulus G