Bear in mind that if you're working with a fantasy world that's vaguely equivalent to medieval Earth, map makers might not necessarily even be aware that they live on a globe, so the issue of projection becomes moot. The entirety of the world may not even have been mapped. The map could even be designed to reflect things other than perfect geographical accuracy, such as the centralised strength of an empire - as was the case for many real maps in our history. Many of these maps were all kinds of different shapes and sizes, depending on what the map was designed for and what kind of materials were available. Something like that might be a more characterful and immersive role playing prop than a geographically and scientifically accurate map of the entire world. Maybe something to bear in mind.