The peculiarities of the propagating transverse waves observed in the solar corona with the Coronal Multi-channel Polarimeter ( CoMP) indicate the existence of fine field structuring in the coronal density. We present results of numerical simulations studying the evolution of a localised transverse magneto-hydrodynamic wave in a uniform magnetic field. We consider two initial low plasma-beta equilibria: one with a homogeneous density, and one with a field-aligned dense structure ( such as a loop or a plume). The perpendicular localisation of the wave strongly determines the angular distribution of the energy propagation. If the perpendicular scale of the wave is significantly smaller than the parallel scale ( e. g. wavelength), as established by CoMP, the wave develops as an oblique fast magneto-acoustic wave. In an unstructured medium, the energy of such a wave is transferred mainly across the magnetic field. However, it is possible to channel the energy of the transverse wave along the magnetic field in the presence of a field-aligned density enhancement. We conclude that the CoMP results provide an independent seismological proof that the corona is structured in density in the perpendicular direction.