Using femtosecond time-resolved X-ray diffraction, we investigate optically excited coherent acoustic phonons in the Weyl semimetal TaAs. The low symmetry of the (112) surface probed in our experiment enables the simultaneous excitation of longitudinal and shear acoustic modes, whose dispersion closely matches first-principles calculations and previously measured elastic properties. We find an asymmetry in the spectral lineshape of the longitudinal mode that is notably absent from the shear mode, suggesting a time-dependent frequency chirp that is likely driven by photoinduced carrier diffusion. Our study underscores the benefit of using off-axis crystal orientations when optically exciting shear deformations in topological semimetals, allowing one to transiently change their crystal structure and potentially their topological properties.