it doesn't seem like SH is actually a "doing" sort of creature. It gives orders and tells people information, but it hasn't actually killed anyone (IIRC). SH has hurt a DF Whitecloak and punished DF Mesaana, but that's it. So I think that SH really only deals with/harms creatures of the Dark, and *helps* to destroy the Light. I'm pretty sure that Elza was the one who knocked out or killed the AS guarding Rand, the Bands, and the CK.
The best support for my idea here is that SH could've taken or booby-trapped the CK, to the Shadow's great advantage.
Still, if all the "rules" and "restrictions" about SH and the mystery of Asmo's death didn't apply (read: if we were just going by the books), I'd think SH is a great candidate.