Thanks for your note, Jane. Interestingly, the quotation attributed to Nathaniel Hawthorne is genuine.

Date: 1860
Book Title: The Marble Fann, Or the Romance of Monte Beni
Author: Nathaniel Hawthorne
Volume 1
Houghton, Mifflin and Company, Boston, Massachusetts
Database: Google Books Full View

https://books.google.com/books?id=m-PhulwpAw4C&q=+%22Time+flies%22#v=snippet&

[Begin excerpt]
“I may have known such a life, when I was younger,” answered the Count, gravely. “I am not a boy now. Time flies over us, but leaves its shadow behind.”
[End excerpt]

The article about “Time flies like an arrow. Fruit flies like a banana” mentions the following, as you have already seen. In 1690 the simile about time appeared in a religious book titled “The Pleasure of the Mind; Or, the Foretast of Happiness”:

[Begin excerpt]
... for the time flies away as swift as a Bird of the Air, or as an Arrow out of a Bow.
[End excerpt]

In 1816 the precise expression “Time flies like an arrow” appeared in “The Infidel’s Text-Book, Being the Substance of Thirteen Lectures on the Bible” by Robert Cooper who described the following statement as a Chinese proverb:

[Begin excerpt]
“Time flies like an arrow; days and months like a weaver’s shuttle.”
[End excerpt]