Yeah, after the first top tower falls often leaves you feeling a touch useless, but really, that is the point where you put on your farm boots and either hard push the lane if going for a proxy style or power farm everything in sight while you wait to get past your power slump. Singed is a great splitpusher because of his wave clear and the difficulty of chasing him, so most of the time I'd just push and farm (although I prefer to not feed as singed, since this build takes a lot of gold and being dead doesn't help you get past your slump any sooner).
You really shouldn't be able to fight most top laners with this build until you are close to full build and have your Rylai's+Liandry's combo, but you can simply hard push a wave and then run off before they can do anything. As singed, you want to avoid confrontation for as long as possible in the match, so staying away from a full on 1v1 fight is your goal. if you are in a team fight, your job is usually to peel diving enemies off your carries with fling and mega adhesive and ideally get the enemy to try and chase you for a kill rather than your allies. if they ignore you, you can rush their backline and try to kill them before kiting away again. You're more of a skirmisher than a hard engage champion, since you just want to tag your enemies with poison and then get away, then go back in, in a very skirmish heavy dance until you annoy them enough to go after you instead of you going after them. Everybody knows not to chase singed, but most of the time if you annoy them enough, they can't help themselves.
Also, the reason I like FH better is that your build already has a ton of health because of your passive (usually around 3k mana with full build at level 18 for about 750 health), so having higher flat armor is generally more useful to me. if you need to kite/stick to a target better, Randuin's is the better option for the active. if you are just buying it for the durability, FH is better (especially since it gives you CDR, health, and AP because of your passive and Seraph's). FH isn't flat out better than Randuin's, it is just better for my style, where if you feel like you get kited too much, Randuin's may be just right for you.