While becoming an Animagus was usually done with a potion, Jon had found out it was but a crutch to make the process easier and safer. Shamans and druids of old did not use it to connect to their inner animal, and even if Jon wanted to use it, most key materials simply did not exist on Planetos. Without it, it was very hard for a wizard to enter their inner world on their own, let alone connect with their inner animal or keep even a small semblance of their mind in the process.