PSA: With new patch, if your enemy top picks Singed, play Evelynn top.

I know it sounds trollish, but here is why it's not only viable, but optimal.

She already was a great choice vs singed in lane. Her speed with W means that singed can never catch you with fling and he can never damage you with poison because you can farm at range with Q. Since he can never hurt you and is set back by your incidental Q damage, he is forced to proxy to be useful. Just stay out of melee range, which Eve can easily do. If he is adamant about staying in lane, you can poke him down with Q, then flash/ignite/E for the kill. He is much squishier now with the passive change, as well. The only time you are ever in danger is from a jungler gank at low levels before you get waveclear and sustain, so place wards and be careful. Personally, I rush Tiamat into Hydra and Trinity Force, and just facetank waves with lifesteal while regening mana between waves with passive, while singed proxies past my first turret.

With the new Grounded debuff on his glue, many champs who previously countered him now are much riskier picks. Eve's W is not a dash, but a slow cleanse/ghost effect, which completely counters every aspect of Singed's kit, and Q max with Tiamat ensures you can clear even faster than him, and roam to mid or enemy jungle while he's trolling past first turret. An end game Eve with good CS and a tanky DPS build is going to outperform Singed in teamfights. Even better if you can use her stealth to make picks in other lanes while Singed trolls and proxies like they usually do.

The only way you can lose is if your team insists on fighting / chasing singed. Communicate with your team :)