Instead of Hedwig being bought in Diagon's pet shop, Harry either buys or is gifted by Hagrid the magical equivalent of a Honey Badger (could be a magical Komodo Dragon, an actual Honey Badger or Wolverine, a swan that has more in common with a velociraptor, et cetera).

​

Harry immediately falls in love with his "cuddly, new best-friend", which warms Hagrid's heart, thinking Harry is definitely a "good lad" if animals love him.

​

Everyone else who recognizes what it is robe-shittingly terrified, and those who don't quickly come to fear it from its casual yet terrifying behaviours, such as hiccoughing corrosive acid or having shifting scale or fur patterns that hypnotize people into doing simple stuff, like walking into doors, et cetera.

​

Harry is either oblivious or genuinely doesn't understand why "cuddles" terrifies people.