Frank was going through a very difficult time during the early 50s. His voice was still similar to his early 40s style, but that would change in due course. A few years later, he was back with a vengeance.
This was a few years before he recorded the famous version when he starred as the title character in the film adaptation of “Pal Joey”. 1952 was in fact the same year as the Broadway revival of the show starring Harold Lang, Helen Gallagher and (from the original 1940 production), Vivienne Siegel). This revival was a much bigger hit than its predecessor so the song was probably hot when Sinatra performed it.
I was so glad when Frank took off that ridiculous hat- probably the only time he didn’t rock any hat he wore🎩 but the important thing is .. the voice , the interpretation of whatever he sang🎶