The best picks outside of lane to counter Singed include Nilah, Jinx, and Sivir. These are all good at countering Singed with win rates over 57%. Even if these Singed counter picks are not chosen in your lane, it's not smart to play him into these matchups. They will often destroy Singed.
Conversely, if the opposite team choses either Swain or Skarner, Singed mains should seriously think about picking him, as he easily wins against these champions with win rates over 55% against each ofthem.