Remember the last time you gave a tanky AP champion %HP damage?
Maokai was ridiculous for how many patches? And now he's just kinda mediocre at everything.
Do you want the same thing to happen to Singed, Riot? I get why you think this is a good idea (tanks need some reason to keep focusing them, and they need to be tough to not die. Therefore, giving them damage that scales on the enemy's health means they get to be damaging and build tanky) but it's not nearly that simple. As basically every bruiser has showed us, being both tanky and damaging is a balance nightmare. This would encourage him to be even more of an unkillable jerk then he already is, and it doesn't even have to do with his main strength (he's difficult to run away from or catch; his entire kit reflects this idea).
I get that you want to buff him in some way, but this is not it. %HP damage is bad for the game. Please don't do it more.