As theatre critic for the Wall Street Journal, Terry Teachout has seen more than his share of had solo shows, partictilarly the all-too-familiar genre of the historical biodrama. That’s precisely not the sort of play he wanted to write with Satchmo at the Waldorf, running at Shakespeare & Company Aug. 22-Sept. 16 in Lenox, Mass., then at Long Wharf Theatre in New Haven, Conn., Oct. 3-Nov. 4, with Gordon Edelstein directing and John Douglas Thompson in the title role.

“This is not what Gordon calls a ‘taxidermy play,’ where someone sits around and talks about what a great guy he is,” says Teachout, who wrote an acclaimed 2009 biography of Louis Armstrong, Pops. It was a reader of that book who suggested to Teachout via e-mail that “there might be a play in it. That had never occurred to me. No writing of plays had ever occurred to me, in fact.”

Teachout did have one prior experience as a dramatist, writing the libretto for the 2009 opera The Letter with composer Paul Moravec. “Obviously that knocked something loose in my head,” Teachout concedes. And so, during a 2010 residency at the Winter Park Institute of Rollins College in Florida, Teachout hammered out a first draft, using as a jumping-off point a memorable photo from Pops.

“The photo shows Armstrong sitting in his dressing room in Vegas about six months before his death; he’s in his tux, and he’s looking old and tired. I imagined that the play might take place in his dressing room at his last gig.”

A theatre-savvy friend who read the draft offered a crucial piece of advice, pointing to the solo plays Teachout himself had admired most in recent years, including Heather Raffo’s Nine Parts of Desire, Stephen Lang’s Beyond Glory and Doug Wright’s I Am My Own Wife. The common element? All had more than one character. Immediately, says Teachout, “I thought: Glaser.”

Joe Glaser, Armstrong’s mobbed-up manager and close friend, now takes up roughly a third of the stage time in Satchmo at the Waldorf. His presence not only rounds out the story, since, as Teachout says, “Armstrong is an unreliable narrator, and Glaser tells us things that Armstrong didn’t know.” Glaser’s inclusion also makes the play something other than an easy bit of imitative gimmickry.

“The idea is for the actor to be able to switch on a dime between the two characters,” says Teachout. “The key to it is that he is crossing a racial line to do it.”

For his part, Armstrong seemed to trip across the color lines of his day with smiling ease, but of course it wasn’t so easy. His outsized charm, in fact, belied a strong will and a fierce temper. Both are on display in Teachout’s uncensored take on the backstage Satchmo. As the playwright says of his subject, “He never said ‘motherfucker’ on ‘Ed Sullivan.'”