In this article we explore the effect of chemical potential at zero temperature in the implementation of in-medium effects in the perturbative sector in finite energy sum rules. For this purpose, we explore the axial, axial-pseudoscalar and pseudoscalar current correlators involving charged pions. The inclusion of non-normal ordered condensates with chemical potential effects in the operator mixing is considered. As a result, the contribution of the operator mixing with chemical potential dependence cancels all the explicit chemical potential contribution of the perturbative sector, aligned with the so-called "silver blaze problem". We find an abrupt transition when $\mu=\sqrt{s_0}/2$, with $s_0$ representing the hadronic continuum threshold. Exploring beyond this critical chemical potential we found similarities with low-energy effective meson models at high chemical potential.