He spent the first 10 full seasons of his 21-year career with the Montreal Expos and then moved on to the Chicago Cubs for his one MVP year, 1987, and the next five seasons. He had already hit 399 of his 438 career home runs by the time his career wound down in stints with Boston and Florida from 1993-96.
Dawson appears to be leaning toward the Cubs, having said before the holidays when an MLB.com reporter who covered him in Chicago asked him about the cap, "I think you know the answer to that. And for a lot of obvious and personal reasons."
Referring to his departure from Montreal, Dawson said on Wednesday, "For me, it wasn't about a monetary issue. It was about respect."
Whether it's the Cubs or Expos for the man they called "Hawk," this Cooperstown cap conundrum is hardly baseball's first.
Late pitcher Jim "Catfish" Hunter, for example, enjoyed so much success with the Oakland Athletics and New York Yankees that he decided to be remembered with a blank cap bearing neither logo. Nolan Ryan, meanwhile, played more games for the Houston Astros and California Angels than he did for the Texas Rangers, but he went into the Hall as a Ranger because he got his 300th win and 5,000th strikeout in that uniform.
Reggie Jackson won three World Series championships with the A's but went in as a Yankee, for whom he won two rings and garnered the nickname "Mr. October" for his stellar 1977 Fall Classic home run binge.
Dave Winfield spent the bulk of his Hall of Fame career in a New York Yankees uniform, but he elected to be portrayed in the cap of his first team, the San Diego Padres.
The Hall of Fame took over the decision-making process for choosing the cap after the 2001 elections and does so after consulting with the player, according to Hall spokesman Brad Horn.
Hall of Famer Gary Carter, for example, was inducted in 2003 and is depicted in Cooperstown in the cap of his first team, the Expos, even though he won his only World Series ring as a member of the New York Mets.
As for Dawson, the answer to the cap question might be answered as early as Thursday, but the Hawk didn't want to talk about it Wednesday.
"Right now, I'm just content to take this all in," Dawson said, "and worry about that later."