The last time Paul Shaffer went on a full-fledged rock ’n’ roll tour, it was 1980 and he was playing with the Blues Brothers. What he remembers most about the experience, more than any hedonistic misadventures with John Belushi and Dan Aykroyd, is traveling from city to city with a band of veteran R&B musicians on a fragile, twin-engine propeller plane.

“We’re with contemporaries of Buddy Holly and Otis Redding,” Mr. Shaffer recalled recently in his dry delivery. “Somebody said, let’s at least write a song about an air disaster so that our families will have some sort of annuities.”

He began to sing the lyrics from “Air Disaster,” a preflight song the entourage would perform to ward off evil spirits:

Rock tragedy

All they had to do was spend a couple more g’s

Rock tragedy

Including several members of the M.G.’s

That was half a lifetime ago for Mr. Shaffer, 67, who came from Fort William, Ontario, to New York in hopes of becoming a great session musician. Instead, he spent more than 30 years alongside David Letterman as his wisecracking sidekick, keyboardist and bandleader on NBC’s “Late Night” and CBS’s “Late Show.”

Now, nearly two years after Mr. Letterman stepped down from “Late Show” in May 2015, Mr. Shaffer is about to step out with his first major post-TV project. On Friday, March 17, Sire Records will release a self-titled album from Mr. Shaffer and his longtime colleagues, who are once again calling themselves the World’s Most Dangerous Band (as they did on NBC).