Abstract Optical skyrmions are members of the emerging topological branch of solid-state physics and photonics, allowing for control over topological light textures through light-matter interactions. However, in nanophotonics their practical application has been severely limited by high inherent losses in plasmonic materials, resulting in the lack of tunability between different topological properties. Here, we utilize the strong dispersion of silicon carbide thin films to realize highly confined surface phonon-polariton skyrmion lattices, which we image via near-field microscopy. We experimentally demonstrate topological tuning between bubble- and Néel-type skyrmions, a unique advantage that polar dielectrics offer over most existing approaches. Changing the excitation wavelength by only 10% switches the skyrmion type, revealed by examination of the skyrmion number density contrast. Analysis of domain wall size and steepness in analogy to magnetic materials also confirms this transition. Our results are a starting point to investigate other topological features in phononic systems such as merons, skyrmion bags, and other complex structured light fields. Furthermore, strong light-matter hybridization and nonlinear effects owing to anharmonicity of the phonons may be observed in the future, possibly leading towards the discovery of polaritonic skyrmion-skyrmion interactions and hence applications in topology-based information processing.