I spoke with a tailor recently who recounted the days back in the 1960s when he regularly made white, unlined sharkskin suits. He also wore them himself. Apparently they were quite the thing to wear in Los Angeles at that time. Unfortunately, he said the fabric is no longer available today. If anyone has a picture of a white sharkskin suit, please let me know.
By coincidence, there is a new book called "The Man in the White Sharkskin Suit", which is a memoir of life in Cairo before and after the Second World War (review, book). The title refers to the author's nattily dressed father.