In this Letter, we prompt a novel, to the best of our knowledge, method based on transmission matrix decomposition with wavelets to engineer the speckle morphology behind disordered media. By analyzing the speckles in multiscale spaces, we experimentally realized multiscale and localized control on the speckle size, position-dependent spatial frequency, and global morphology by operating on the decomposition coefficients using different masks. Speckles with contrasting features in different parts of the fields can be generated in one step. Our experimental results demonstrate a high degree of flexibility in manipulating light in a customizable manner. This technique has stimulating prospects in correlation control and imaging under scattering conditions.