The big difference would have been the image and the persona that the then Cassius Clay was projecting to the world. Being the World Heavyweight Champion was a huge deal in the 1960's, Ali would not have been able to tell the world "I am the greatest" one of the most memorable phrases in world sports history. He would not have fought Liston in 1964, he would not have received the publicity he eventually did get after becoming World Champion, his conversion to Islam may have gone unoticed and maybe his controversial Army call up might not have happened. Ali was good, very good, i often think that at times he even distracted himself going into fights (Frazier 1 being an example) Cooper being another, Ali was there to impress the British public and let them know just exactly who he was and what he will become, he took Cooper for granted and got hit with the hammer.
If that left hook was delivered just 30 seconds earlier history would've being altered dramatically, it is conceivable to believe that Ali might not have recovered from that defeat? Many fighters take losses badly and who knows how it would've affected Ali to lose so early in his career? Ali did take notice of that left hook that got him, he was very wary after that and fought some big punchers and sluggers keeping his distance and using that famous jab to perfection. In some ways Enry's hammer helped Ali to become a better fighter. There is no doubt that Ali had utmost respect for Henry Cooper and he knew his career could've have been very different had 'Enry won.