Wear the girdle and stockings if you like. If you are wearing a bra anyway, a girdle shouldn't be any more or less suspicious.
You might want to wear a slip underneath your costume, for both practical reasons (prevent showing too much from see-thru or if your skirt gets caught on something etc.) It also adds to the vintage-ness of your outfit. It would also add another "barrier" if someone wanted to see what is underneath (as unlikely as that would be.)
