Mihawk will be alright. Just because Roger was the top dog doesn't make Rayleigh, Whitebeard, Linlin or Garp weak. They acknowledge Roger as nr 1 even though they were all in the top 10.
Same thing with Mihawk. He knew WB was nr 1, no shame in being below the great man himself (but I believe Mihawk recognized immediately during the war that WB was not nr 1 anymore). And no shame in acknowledging that Luffy will become stronger than himself, he is the next Roger after all.
It's like being a tennis player and humbly acknowledge Djokovic, Nadal or Federer as the nr 1 whilst you are in the top 10 yourself or spotting the new up and coming GOAT candidate. Real recognizes real.