I have not played such levels yet so my opinion may not be very informed. I actually would've thought disarmed traps would just disappear from the level, though I suppose if a level has so many of them scattered throughout, I suppose it's conceivable sometimes one can lost track of where they were and don't want to have to rely on rewind/fast-forward to remind yourself.
Clearly an extra broken sprite is the right thing to do (or potentially even an entire looping animation sequence, if the designer wants to depict a smoldering wreck for example), but perhaps should be optional even if highly recommended for the style designer.
X-ing out the trap or other such indicator seems like a reasonable fallback. I suppose it can be ugly but at the same time, I think you'll find it difficult to come up with something generic that will work satisfactorily across the variety of sizes you may come across for triggered traps. (But hey, do try to prove me wrong on that.) I mean, there's a bit of diversity just looking at L1's traps already. And besides, isn't the whole point of a lemmings game to vandalize the level in order to rescue the lemmings?
How important is it really that the level remains absolutely free of ugliness at the end of it all, when the terrain has probably already been bashed, mined, and blown to bits and unnatural cubes, platforms and staircases (some of which are probably also bashed/mined/blown/...) scattered all about?
Maybe an option to simply hide disarmed traps if ugliness is such a bother to some (note: I'm assuming there is no re-arming or anything of that sort currently in NeoLemmix). I also suspect some users can keep track directly in their head of where the likely-few traps they spent effort figuring out how (and which ones) to disarm, without a constant visual reminder, so might not be that crazy to allow them to hide the disarmed traps if that's what they prefer.
Displaying with translucency or grayscale could also be potential alternatives that may be less ugly, though presumably may sometimes be too subtle.