Chiral Majorana modes, a key ingredient for topological quantum computation, arise on the surface of a three-dimensional time-reversal-invariant topological superconductor when a magnetic field induces a sign-changing surface mass. In practice, the orbital response of the superconductor tilts the surface spectrum and overwhelms the Zeeman term as the field grows. Here we show that magnetic impurities on a spherical surface can instead generate this mass term through their exchange coupling, so that only a weak field is required. The Ising surface Majorana modes mediate a ferromagnetic Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, derived here on the curved surface, that orders the radial impurity moments into an inversion-breaking hedgehog at zero field. An axial field instead stabilizes a domain wall across which the radial magnetization reverses sign, leaving a single chiral Majorana mode along the equator and realizing an inversion-protected second-order topological superconductor.