Disclination lines in chiral nematic liquid crystals exhibit larger geometrical diversity than their counterparts in ordinary nematics and form rich entangled structures in systems with dispersed colloidal inclusions. Numerous metastable and stable states separated by low energy barriers allow for simple rewiring of the braids. Introducing a new visualization scheme where variations in splay, bend and twist deformations are followed separately allows us to display the effect of chirality on the director profile of the disclinations, and to uncover the mechanism of their rewiring. We demonstrate the richness of structures by performing a survey of all possible disclination structures that entangle a pair of homeotropic silica microspheres in a π-twisted cholesteric cell using numerical free-energy minimization and laser tweezers assisted microscopy. We analyze their stability against spontaneous rewiring and trace the stability differences to the local effects of chiral environment. We compare the predictions to the experimental results and discuss the differences between both approaches.