Kordell Stewart on Thursday told me Buffalo must stick with Edwards, who has been struggling mightily for four games.
But on "NFL Total Access," Woodson said the Bills should make a switch for Sunday's game against the Kansas City Chiefs because the playoffs are on the line.
"You treat a quarterback just like a DB, a tackle, a tight end, a receiver," Woodson said. "If they're not playing well, you've got to give your team the best opportunity to win.
"I understand you don't want to play head games with a young guy like this, but you still owe it to your team to give your team the best chance to win and put those guys on the field."
While chatting with ESPN analyst and former Tennessee Titans general manager Floyd Reese on Friday, I asked what he thought about Edwards' amazing drop off.
Over the past four games, Edwards has thrown three touchdowns and eight interceptions.
"People want to talk a lot about the concussion" Edwards suffered in Week 5 against the Arizona Cardinals, Reese said. "I don't see that in the same vein. The concussion probably has come and gone.
"As it is with a lot of young quarterbacks, he's a reflection of what the team is doing well. They're turning the ball over. There's an inappropriate number of fumbles. They're not running the ball well. They're not getting the big plays out of the receivers like they did the first seven games of the season.
"A young quarterback can't carry a team in the NFL yet. He's so young. He's just a reflection of what's going on with everything else. If they could run the ball, then he could play-action pass, cut down on his interceptions the times he's getting hit, get the ball to Lee Evans more."
Reese said he thought Edwards was playing scared by the end of the first quarter of Monday night's loss to the Cleveland Browns.
As for Bills coach Dick Jauron's decision to run three straight times before unsuccessfully trying a game-winning field goal, Reese said, "Heck, he was probably scared to death to throw the ball, too."