The actual use of the term predates Q's example by quite a bit...
From Word Origins: MONKEYSHINES; MONKEY BUSINESS - "Foolish or mischievous activity. One assumes the sly, alert, advantage-taking behavior of the monkey gave rise to this notion." This source cites a use of the phrase "monkey business" in a 1904 Brooklyn Standard Union newspaper article. From "The Dictionary of Cliches" by James Rogers (Ballantine Books, New York, 1985). A second reference has earlier dates for the phrases. " 'You may have barefooted boys cutting up 'monkeyshines' on trees with entire safety to themselves,' observes one of the earliest writers to use 'monkeyshines,' monkey-like antics, which is first recorded in 1828. 'Monkey business' was recorded a little earlier, at the beginning of the century, both words suggested by the increasing number of monkeys imported by America's growing circuses and zoos." From "Encyclopedia of Word and Phrase Origins" by Robert Hendrickson (Facts on File, New York, 1997). In addition, a young black comedian in the U.S. said older blacks had accused him of "cutting monkeyshines" in front of a white audience - acting in a stereotypical demeaning manner to get laughs.
Additionally, the word 'shines' in this context is described as meaning "... A "shine" is a "prank or caper." As in "She cut a shine". From "Southern Mountain Speech" by Cratis D. Williams (Berea College Press, Ky., 1992)