Twelve years on, Shaw is hoping to re-enact Davidson's snatch and grab raid by pushing himself into the running to partner Paul O'Connell in Saturday's first Test against the Springboks in Durban.
McGeechan told all the British & Irish Lions players on the first day they met that he would not select his Test side until after the six warm-up matches had been played. Tuesday's game against the Southern Kings in Port Elizabeth in the sixth game and Shaw is taking the coach's words at face value.
"Back in 1997 Jeremy Davidson played against the Emerging Springboks on the Tuesday and forced his way into the Test side at the end of the week," recalled Shaw.
"Ian mentioned that to us all in training ahead of the game against the Southern Kings ansd we all believe him when he says he won't be picking the team until Wednesday. We've all got one final chance to stake our claims for a test spot.
"But while we all have personal ambitions, the most important thing is to keep the winning streak going and play for the team."
Shaw is on his third Lions tour and has still to make a test team. He managed to play for England in the 2007 Rugby World Cup final, having sat out the 2003 final in Sydney, and now wants to tick another outstanding box in his career.
"Realistically I feel as though I'm probably playing for a place on the replacements bench, but I know that a huge performance could still get me into the team," said Shaw.
"The coaches have all been very frank with us from the outset. I was told after the first game that I hadn't played well, but I was complimented for making an impact when I came on against The Sharks.
"Their frankness and honesty is a real positive for the team. It has been difficult for me to try to impress.
"I hadn't played for five weeks before the first game and then I've only had appearances off the bench. I haven't played in a test for the Lions yet and that is something I hope to rectify on this tour.