I can't find reference to a "Special Trap".
I find a "Super Trap". Double barrel hammerless.
As soon as the action is opened, it cocks, so obviously it can be unloaded while cocked.
The single-barrel hammer gun, the Champion, appears to have been made in "Trap" grade. If that's the one you mean, I don't know, but I suspect not.
I just checked with an H&R Topper. When the hammer is cocked, the unlocking lever will not move. I suspect the Iver works the same way.
Safety first? Absolutely. Lower the hammer.
Meddle not in the affairs of dragons, for thou art crunchy, and taste good with catsup - George of Lod, Year of Our Lord 297
I always take precautions.
Beware the Evil Bullet Fairies.