In this work, we present a method to reveal azimuthal whispering gallery modes (WGMs) in a spherical microcavity coated with a nano-meter thick polyelectrolyte (PE) shell and one monolayer of CdTe semiconductor quantum dots. The PE shell deformability was increased through contact of the shell with a salt-containing solution, which changes the mechanical properties of the PE multilayer. The new approach in this experiment is based on the deformation of the spherical shape in a non-contact way using the radiation pressure from a laser beam, which causes the lifting of the degeneracy of the WGMs. Applying radiation pressure results in localised shell shape distortion and splitting of the resonance peaks. The peak shape was modelled on analytical expressions for a distorted sphere demonstrating very good agreement with the measurements. The resonance peak linewidth and splitting parameters can be efficiently controlled by the strength of the radiation pressure and the elastic properties of the surface shell.