Diameter-modulated nanowires offer an important paradigm to design the magnetization response of 3D magnetic nanostructures by engineering the domain wall pinning. With the aim to understand its nature and to control the process, we analyze the magnetization response in FeCo periodically modulated polycrystalline nanowires varying the minor segment diameter. Our modelling indicates a very complex behavior with a strong dependence on the disorder distribution and an important role of topologically non-trivial magnetization structures. We demonstrate that modulated nanowires with a small diameter difference are characterized by an increased coercive field in comparison to the straight ones, which is explained by a formation of topologically protected walls formed by two 3D skyrmions with opposite chiralities. For a large diameter difference we report the occurrence of a novel pinning type called here the "corkscrew": the magnetization of the large diameter segment forms a skyrmion tube with a core position in a helical modulation along the nanowire. This structure is pinned at the constriction and in order to penetrate the narrow segments the vortex/skyrmion core size should be reduced.