The composition of dense matter in neutron star interiors remains uncertain, with the possible appearance of the non-strange $\Delta$ resonances providing an important source of theoretical uncertainty. In this work, we investigate the gravitational wave signatures of hyperonic neutron stars containing $\Delta$ baryons within a density-dependent relativistic mean-field framework based on the DDME2 parametrization. Within this framework, the baryons interact among themselves via mesons. For $\Delta$ baryons, the interaction is uncertain to date. We investigate how variations of the scalar and vector $\Delta -$meson couplings, subject to (x_{}-x_{}=0.2), modify the tidal properties and inspiral gravitational-wave signals. We find that the allowed variation in the $\Delta -\sigma$ coupling leads to substantial changes in the tidal properties of the neutron stars, which in turn leave distinct imprints on the gravitational-wave waveforms, particularly in their frequency evolution, accumulated phase, and strain amplitude. These waveform differences arise through changes in tidal deformability and are not unique signatures of $\Delta$ resonances. Future gravitational-wave observations may therefore constrain the $\Delta -$meson couplings within the adopted dense-matter framework, subject to degeneracies with alternative EOS models.