If you want both (a nice-looking postcard that reflects your feelings) here are some good news. Things have changed and now you have some good options..., well, at least two good options to be sincere using a card.
You can send a "Wrong Card" for free via email (they are online and they have cards for any ocassion) or you can buy at Etsy "Courtesy Cards" by Gramkin Paper Studio that are like business cards, but with the purpose of getting rid of undesirables in a very polite way.
Of course these cards are meant just for people with sense of humor. Incorrect use of any of them could lead you to trouble!