The ex-England hooker, 57, won the competition with Devon in 2004 as a player and as coach in 2007, and played in Cornwall's triumphant 1991 campaign.
Dawe has been Cornwall head coach since 2013, leading them to victories in the 2015 and 2016 Twickenham finals.
"It's a nice local game for me, but I'm travelling as a Cornishman," he said.
"I'm 100% behind Cornwall, there's no emotion at all."
The game will be played at Ivybridge on Saturday, with Cornwall favourites as they continue their pursuit of a hat-trick of County Championship titles against a Devon side who were only promoted to Division One because of a restructuring of the competition.
Devon head coach Dan Parkes played under Dawe at Plymouth Albion, and acknowledges his side are underdogs.
"It's going to be hard, the boys are going to be up against it," he told BBC Sport.
"For Graham the pressure is on, but I'm sure they'll get to their third final.
"The better we can do, the more likely we can attract players next year. Players play for Cornwall because they know they have a great chance of reaching Twickenham."
Graham Dawe says he has "no emotion" ahead of his Cornwall side's County Championship game at Devon, who he previously played for and coached.