Byrne stepped in during the 2003 RBS 6 Nations after Wood's injury and impressed. And now Wood has retired and the Leinster hooker is in pole position for the role.
"He was a fantastic icon for Irish rugby," said Byrne, six months older than his famed predecessor.
"Only Keith Wood could do what he did. He played a specific style of rugby which he was the best at.
"I definitely don't try to emulate him. I just play my own game.
"But I've never been as fit or as strong. When I first got into the Irish squad I was getting to the stage where I was thinking, 'Oh my God, so much time has gone by. The rest of my career could go by, and I could get no cap'.
"Luckily it came in 2001, and I'm at the stage now where I never thought I would be - where I can genuinely say that, even with the seven or eight-year wait, I wouldn't change a thing."
However, Byrne is not complacent and does not assume he will automatically slot into the Irish front row.
Munster's Frankie Sheehan - another of Wood's long-term understudies - and rising star Bernard Jackman can also lay their own claims.
"As long as he [Wood] stays retired, the place is up for grabs now," admitted Byrne. "I don't think it's simply a case of stepping up and filling the gap.
"If there had been an international soon after the World Cup it would have been easier for me maybe, but now it's up for grabs."