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In this work, we develop a theory of (meta)stable states of N\'eel-typeskyrmions in weak nonuniform magnetic fields. We claim a novel ansatz formodeling the non-symmetric magnetization that can be implied for both analyticsand numerical simulations. Our theory accounts for changes in the size skyrmionparameters and also includes deformations from the centrally symmetric shape.The ansatz streamlines the analytic calculation of the skyrmion free energy,enhancing the efficiency of the minimizing process. Performing the minimizationin two stages, one can find all the minima, global and local, of the freeenergy, discovering the stable and metastable states. We apply the developedmethodology to investigate the (meta)stable configurations of skyrmionsinfluenced by the stray field of a Pearl vortex. Our study reveals thedependence of skyrmion spatial parameters on the vortex field effectivestrength and presents a phase diagram identifying regions where metastableconfigurations are predicted. Corroborated by micromagnetic simulations, ourfindings offer a detailed perspective on the interaction between magneticskyrmions and superconducting vortices.

Deformation of a N\'eel-type Skyrmion in a Weak Inhomogeneous Magnetic Field: Magnetization Ansatz and Interaction with a Pearl Vortex