The flaming greatsword's too slow to be really effective.
My best strategy for soloing him was to backpedal while spamming the flamarang attacks
This. You
need a high-damage attack to kill him before time runs out - I don't believe anything below Molten packs enough of a punch. I killed him with a Flamarang and full Shadow set, bringing him down with ~1:30 left before morning. (And 20 large health potions, but that's incidental - it's time, not health, that'll kill you.
)
Unholy arrows + Demon Bow
might work, only because the lower damage of the bow is offset by the arrows' piercing ability. I believe the boss has, what, 7 defense? If so, you'll be dealing (13 + 8 - 7) = 14 damage per hit, probably landing double hits thanks to pierce-through, for ~28 damage per shot. Assuming that's true, you'd need somewhere around 215 hits, assuming they're all double hits and I haven't screwed up any numbers. That's a
lot of Unholy Arrows - accounting for misses and non-double-hits, I wouldn't attack him with any less than a full stack, assuming you're very lucky with arrow recovery during the fight. A stack and a half would be preferable.
...yeah, I'd descend into Hell, or at least get one of the top-tier weapons from the Jungle, before even
considering attacking Skeletron.