Zach Deputy never found exercise fun. But when his weight tipped past 400 pounds, he knew he needed to move more. Running was uncomfortable. CrossFit sounded like torture. And low-impact activities like golf seemed boring until the singer-songwriter’s tour manager introduced him to disc golf six years ago. Instead of using a ball and club, players attempt to throw a Frisbee-like disc into an elevated metal basket in the fewest throws possible.

On his second disc golf outing he landed a toss from 150 feet away. “From that...