THE IPOD SHUFFLE is dead, but it still has ardent admirers. While Apple discontinued its tiny MP3 player in 2017, refurbished devices endure on eBay, a happy hunting ground for music fans who want to enjoy tunes without a cumbersome phone or the distractions it subjects them to. I’ve held on to my Shuffle for those exact reasons—and it doesn’t hurt that it looks cool.

But there’s a new cool kid in town: The Shuffle has clearly inspired the Mighty, a device which debuted last year and recently got an update in the Mighty Vibe...