Happy to see a forum for this underappreciated program!
Yes, it was called "Secret Agent", and I think it aired Saturday nights. My mom and stepdad never missed it, but I was in my early teens, and it was really above my head at the time. I had no interest in its original airings beyond the Johnny rivers theme song, which I thought was awesome at the time.
However, when I looked for the series in the DVD age, I was surprised to see it packaged under the UK name (it immediately brought to mind "Dangermouse", which I thoroughly enjoyed in its rerun on Nicolodeon in the 90s).
I was also very taken with the British theme music ("The Wire"), and thought that we on the American side missed a very nice piece of music.
In 2007, I watched via Netflix the entire 1964-67 series, and was only marginally aware of a season of half-hour programs four years prior to the more popular full-hour series.
I think at the time, the 1960 season was not available, but recently I became aware of its availability on Netflix and I quickly ran through the entire year's episodes.
Brilliant!
But in its full hour format, it was like going from having a quick snack to having a 3-course meal. Very satisfying indeed. And so I have begun wending my way through the entire, hour-long "Danger Man" DVDs again. Delicious.