  Proximitizing magnetic textures and $s$-wave superconductors is becoming a
platform for engineering topological superconductivity and Majorana fermions by
the means of exchange processes. However, the consequences of orbital effects
have not yet been fully taken into account. In this work, we investigate the
magnetic skyrmion texture-induced orbital effects using a Ginzburg-Landau
approach and clarify the conditions under which they can induce superconducting
vortices. These orbital effects are then included in Bogoliubov-De-Gennes
theory containing the exchange interaction, as well as superconducting vortices
(when induced). We find that the topological phase is largely stable to all
investigated effects, increasing the realistic promise of
skyrmion-superconductor hybrid structures for realization of topological
superconductivity.
