The best champs outside of lane to counter Karthus include Kalista, Lucian, and Aphelios. These champs are all good at countering Karthus with decent win rates over 62%. Even if these Karthus counter picks are not taken opposite your position, it's not smart to play him into these matchups. They will very likely crush Karthus.
Yet, if the opposite team picks either Taliyah or Xerath, you should seriously consider picking him, as he easily destroys these champions with win rates over 54% against both ofthem.