The concept of skyrmions, which refers to topologically stable vector textures and was originally introduced in particle physics, has recently been transferred to various types of fields, including electromagnetic ones. Its potential in optics and photonics stimulates the development of sophisticated strategies for skyrmionic beam shaping, but these are limited to bulky systems, thus hindering the emergence of practical applications. Here we propose and experimentally report on the realization of compact flat-optics skyrmion generators based on the spin-orbit interaction of light. Our approach highlights how the use of unitary wave plates beyond the uniform-retardance condition opens new avenues for the preparation of topological optical states.