The Dead might have been able to harm. (Though I agree they couldn’t slaughter anyone with non-corporeal weapons)
We know of two instances of death occurring. One is the old man that appeared in Rohan, proclaimed some spooky shit about the Paths, and fell on his face dead. Possessed?
The other, a Prince of Rohan who ventured the Paths, came across a sealed door, and was attacked by someone from behind, leaving his legs broken - hence unable to move, he died in the dark, alone. Was it the Dead (Stalking their prey from behind, like we see in ROTK)? Or living Men?
Both are indirect ‘kills’, so the quote of “I doubt their blades would still bite” may still ring true. But interesting regardless.