We demonstrate that spatially engineered magnetic anisotropy can stabilize skyrmion and meron spin textures in magnetic nanodisks even in the absence of Dzyaloshinskii-Moriya interaction (DMI). Using a constrained analytical model and micromagnetic simulations, we show that competing perpendicular and in-plane anisotropies can generate non-collinear topological textures in non-chiral magnetic systems. We further show that DMI and dipolar interactions lift the helicity degeneracy and select preferred chiral configurations; micromagnetic simulations were used to identify physically stable states. These results establish anisotropy-patterned nanodisks as a platform for studying DMI-free topological spin textures and their controllable magnetic response. We also show that arrays of anisotropy-engineered skyrmions can control spin-wave transmission by manipulating their vorticity arrangement, pointing to reconfigurable magnonic elements based on non-chiral topological textures.