The relation between the liquid crystalline textures and the steady shear viscosity has been investigated in cholesteric emulsions, composed of water, surfactants, and cholesteric liquid crystals. Both at the substrate surface and at the surfactant-coated droplet surface, a homeotropic anchoring is enforced to the adjacent liquid crystal. Under a steady shear flow with the shear rate below 100 s(-1), we observed that point defects spontaneously appear, and tend to adopt a regular hexagonal arrangement in the low shear-rate range of 1-20 s(-1). In viscosity measurements, the shear-thinning behavior was found, showing a clear correspondence to the texture change. We estimated the height of point defects in the hexagonal array from the viscosity increase in the shear-thinning, assuming that the shear-thinning behavior is caused by the reduction of the effective gap between cone and plate, owing to the presence of the hexagonal array anchored on the plate. The relation between the estimated height and the measured lateral size of point defects agreed with that of the quadrilateral array, which is formed after termination of the shear. This agreement informs that the shape of a point defect is preserved in both defect arrays, independently of shearing conditions.