The best champs outside of lane to counter Кай'Са include Наафири, Нидали, and Грагас. These picks are all great at countering Кай'Са with decent win rates over 54%. Even if these Кай'Са counter picks are not used in your lane, it's not a good idea to choose her into these matchups. They will most often crush Кай'Са.
Conversely, if the opposing team picks either Галио or Рамбл, Кай'Са mains should strongly think about selecting her, as she easily dominates these champions with win rates over 56% against both ofthem.