Nobody will think less of you if you use wrist watch instead of wristwatch because, well, a lot of people still do, including Google. Google actually isn't a person, but when you search for wristwatch, Google thoughtfully tries to correct you:
That's because Google knows that a search for wrist watch produces about 27,100,000 results, while wristwatch yields a mere 1,780,000 pages.
Not for the first time, The Internet is Wrong. You may have encountered other examples of that yourself. For example, when Hurricane Sandy wreaked havoc across the eastern seaboard of the United States in 2012, rumors of the New York Stock exchange being flooded flew around the Web like tree branches themselves during a storm.
How do I know that Google is wrong? First, over the past century authors of books, who are generally literate people but who also work with very smart editors, have transitioned from using wrist watch to wristwatch—one word. The trend, as evidenced in Google's own Ngram viewer (a service that shows word usage in books over time), has been from wrist watch to wristwatch:
The change from wrist watch to wristwatch in books was striking and fast. In just 10 years wrist watch went out of fashion, to be replaced by wristwatch.
The use of the word wrist watch even feels quaint. Take a look at this news report that appeared in the New York Times on January 27, 1916, and tell me that wrist watch doesn't seem out of place in time:
The other reason we can be sure that it's wristwatch and not wrist watch is that wristwatch review websites, which know a thing or two about wristwatches, mostly write it as one word. Watch experts speak: wristwatch is one word.
As for the future, let's keep our fingers crossed and hope that we never see WristWatch become the norm.