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The magnetic properties of spinel nanoparticles can be controlled by synthesizing particles of a specific shape and size. The synthesized nanorods, nanodots and cubic nanoparticles have different crystal planes selectively exposed on the surface. The surface effects on the static magnetic properties are well documented, while their influence on spin waves dispersion is still being debated. Our ability to manipulate spin waves using surface and defect engineering in magnetic nanoparticles is the key to designing magnonic devices. We synthesized cubic and spherical nanoparticles of a classical antiferromagnetic material Co₃O₄ to study the shape and size effects on their static and dynamic magnetic proprieties. Using a combination of experimental methods, we probed the magnetic and crystal structures of our samples and directly measured spin wave dispersions using inelastic neutron scattering. We found a weak, but unquestionable, increase in exchange interactions for the cubic nanoparticles as compared to spherical nanoparticle and bulk powder reference samples. Interestingly, the exchange interactions in spherical nanoparticles have bulk-like properties, despite a ferromagnetic contribution from canted surface spins.