Definetly use Quality neoprene overshoes but do nt peel them off completelyFor 3km, I would not bother with the hassle and the downsides mentioned above.
Wear an old jean/trouser/jogging bottom whilst cycling, and put your smart trouser on at work.
Edit: You'll also avoid crotch wear on your nice trousers
Leave them still over the shoe plates
This makes it way quicker when you come to put them on to leave work