Let's turn the clock back 60 years...The October 1964 issue of
Coins Magazine. included an article titled "The Captain Cook Commemorative Half Dollar." The piece was written by Robert Van Dyke, the husband of Jane Cartwright Van Dyke. Jane was the daughter of Bruce Cartwright, Jr. - Bruce headed up the Captain Cook Sesquicentennial Commission which sponsored the coin in the 1920s. All that to say, Robert may have had some alleged, inside, family knowledge on the coin that he wished to share via the article.
1928 Hawaiian (European) Discovery Sesquicentennial Half Dollar

In the article, Robert posited that 3,214 of the Hawaiian half dollars were returned to the Mint to be melted, thus leaving a net distributed mintage of 6,786 coins vs. the accepted figure of 10,000. Such a revelation, if true, would have caused quite a stir in the numismatic community!
Unfortunately for Robert, the veracity of his assertion is questionable. I've looked through many US Mint records and have never found supporting documentation for his claim. In fact, information put forth by the Treasury Department/US Mint in the 1930s, 1940s and even as late as May 1963 indicate that zero Hawaiian half dollars were returned to be melted. (The Mint often presented a Table showing the results of past commemorative coins - issue-by-issue - when it testified at commemorative coin bill Hearings - these tables included a column headed "Number of pieces melted.")
Could these various Mint reports have been wrong? Of course. I would not categorize such an ongoing (decades-long) error as likely, however, but anything is possible. Contemporary (i.e., 1928-29) reports regarding the coin's sales indicated strong interest and a quick sell-out which lends credence to the Mint's figures.
From what I can tell, the hobby
did not rally behind Van Dyke's version of what happened to the Captain Cook - Hawaiian half dollars, and continued down the path of a 10,000-coin sellout with 0 coins returned to be melted. It's where we stand 60 years later.
For more of my posts about commemorative coins and medals, including other Hawaiian half dollar stories, see:
Commems Collection.