Just seeing this suggestion but I would definitely be in favor of such a transmog feature.
Now I would not wish to see a complete free-for-all where a morningstar changes to a Holy Avenger or something but I think it would be nice if we were allowed to swap the skin of a type of armor or weapon and apply it to something of the same type. For example applying Shadowhearts armor skin to other armor that can be worn by the character. That way if you find a set of armor that Shadowheart can wear; I could transmog her original skin onto the armor so that she will still look as iconic as when I first met her.
Currently with patch 9 my Paladin is sporting some very nice looking armor and I would hate to lose the look just because I'm forced to equip better generic armor that offers more AC or has an enchantment.
We already have some minor things like being able to hide our helmets but it would be nice if our characters could also retain their iconic looks (if we choose to; it should never be mandatory ofcourse).
I simply love Shadowheart's armor but you almost immediately replace it with generic scale mail shortly after you've met her on the beach.
Such a shame to see all that work get replaced by generic armors down the line. Larian did a great job to make each of these characters look special so it would be nice if they could retain their original appearance for those who wish to keep their characters looking like they do now.
