Assuming Conor is actually on his A game and his motivation Is there.. That's not a good stylistic matchup for Tony.
His best chance obviously would be setting a very high pace, taking him into deep waters and attempting to drown him. Nate wasn't able to do it at 170 pounds though, weighing 185 pounds. Fighting a heavier opponent will absolutely make you more tired as well than one of similar weight. He did get tired but he also managed to go all 5 rounds.
Tony does have more tools on the feet but I don't think It will matter all that much if he's not able to challenge him In the boxing realm. It seems Tony would need to mix up his game and utilize his wrestling, but that's not exactly the aspect of his game which has allowed him to go undefeated for so long. To his credit, Tony's boxing has Improved throughout the years as I'm sure he's aware that's been a weaker aspect of his game.
There'd be a lot of questions, can Tony challenge him on the feet? Is his wrestling good enough to actually get the fight to the ground against Conor? Getting It to the ground doesn't automatically mean he's gonna get the submission either, Conor can grapple. Tony also doesn't have the kind of dominant top control that Khabib does.
He'd likely be punished on the feet and struggle to get the fight to the ground, he'd need to attempt to get the fight Into deep water where he's strongest. Not unlike Nate, Tony gets stronger as the fight goes on.
Nate is a very similar stylistic opponent and body type and his fight with Conor provides a lot of clues as to how the fight would go with some slight differences. Except It's not likely that Tony would be able to challenge him In the boxing and walk through Conor's punches In the way Nate was able to at 170 pounds. Tony does have more weapons but his unorthodox, wild and often reckless style has gotten him into trouble with virtually all of his opponents on the feet. All of which are nowhere near the level of boxer, have the power, precision and counter fighting ability as Conor at his best. Realistically Conor has the perfect style to counter what Tony does on the feet.
Personally I think the fight would depend on which version of Conor shows up. Skill and style wise I think that's a very tough fight for Tony. Although, obviously Tony Is not without his method of victory.