Well according to a Wiki check, found this:
Another legacy of the show is the popularity of the Hawaii Five-O theme music. The tune was composed by Morton Stevens, who also composed numerous episode scores. The theme, which has been performed by The Ventures, is particularly popular with college and high school marching bands, especially at the University of Hawaii where it has become the unofficial fight song. The tune has also been heard at Robertson Stadium after Houston Dynamo goals scored by Brian Ching, a native of Hawaii.
Although the theme is most widely known as an instrumental, it has been released with at least two different sets of lyrics. The first, by Don Ho, starts with the familiar tempo, then settles into a ballad style. The second, by Sammy Davis, Jr., titled “You Can Count on Me (Theme from Hawaii Five-O)”, maintains the driving style of the original instrumental throughout. The Radio Birdman version was called “Aloha, Steve & Danno”. [/i]
So I don’t know exactly whose behind the horns, per se. But the Ventures get the credits.
Of course as well, they did the following song with another group who recorded it also. Up to you to choose your favorite version on this one though:
The Ventures Live: Wipe Out / pixelmuttz.blogspot.com