The round 10 MCG match will raise funds for the Kokoda Track Foundation, which supports the education and healthcare needs of children who live along the famous path today.
Mitchell trekked the 96km journey five years ago as part of the Hawks' cultural induction of new players and said it was an emotional journey.
Kirk said his personal link to the Papua New Guinean trail dated back to his 88-year-old grandfather, who fought in the region during World War II.
Kirk also made the trek in December 2000 and said he still thought back to what he experienced.
"Last night I read back the diary I wrote during the five days I was over there and I had some really vivid memories," Kirk said.
"The one thing that really sticks out is the spirit of Kokoda, and when you talk about the spirit, you talk about the courage and sacrifice and also how the human spirit overcomes adversity.
"There's no doubt that early in my career, it was really poignant.
"To be able to have a match like this, we are really honouring the spirit of the soldiers and their sacrifice, and I'm a big believer we need to keep doing things like this and I applaud Hawthorn for the way they've gone about embracing that spirit."
Both captains will shake hands with Kokoda veterans on the field before the game.
The Hawks will wear a special commemorative match-day 'camo' guernsey, which was launched earlier this month.
"The battle of Kokoda was one of the most significant battles in Australian war-time history," said club president Jeff Kennett at the time.
"Hawthorn deeply respects not only those who fought on the track, many of whom died, but also deeply respects and admires the hospitality and generosity shown to us every time we return to the track.
"This initiative is our way of returning, in part, the generosity and assistance to the young children of the track with these education and health initiatives."
