The sperm whale dove to those incredible depths in pursuit of the giant squid. My grandmother had a piece of the wax like spermaceti. It was in her sewing kit when I was a child. Family legend was that it was found washed ashore in Bermuda where she was born but it was most likely from a candle.
Your grandmother knew what she had. It was most likely Ambergris from a sperm whale. It is know to wash ashore in the Caribbean. If you knew how it was produced by the whale, you might have wanted to wash your hands after you handled it.
