I say: do it. As long as they are worn to work rather than at work you are fine. And when it is raining as heavily as it was today, no one wants to risk ruining a Louboutin on the commute now, do they?
Besides, waving your hosiery under the hand dryer in the ladies is just so last season.
As for which wellies to wear, for me there is no question...
Hunter Original Wellington at the Iconic