Dwarves will die to traps if they get webbed, stunned, or pass out due to pain there. Anything else and they're fine. Toady has it hardcoded so tiredness will not cause a dwarf to fall asleep on a trap tile, in fact, a dwarf will stay awake forever if his only options to sleep are trap tiles (unfortunately, they can sleep anywhere else, so you can't use this to keep them awake unless you have them doing literally nothing).
Technically you could have them smooth and engrave, or channel out the edges of the trap area.
But I just thought of something. Say you have a door set to be interior (i.e. won't block room resize fill) and forbidden, with a weapon rack/armour set on one side and a fully trapped area on the other. Designate the whole area as a barracks and add your dwarves to it (making sure you can drop in food and booze periodically). The traps could be cage traps (for safe capture of any wounded - animals won't bleed to death in a cage if they were injured beforehand, will they?), spear traps (because they don't do any damage unless triggered), weak weapon traps or a mix. Hell, you can have strong weapon traps and turn it into a gladiatorial death match arena, like the tower of destiny idea that people put up before. First person to fall unconscious dies.
Since they would never rest their wounds (unless they passed out and survived), presumably they keep any yellow injuries or worse forever. Which could lead to you having an army of cripples.