I am coming late to this but I am unaware of any Muslim group that rejects Khadija as the first convert. The story of Muhammad's reception of the first revelation and his immediate flight in terror to hide weeping beneath Khadija's robe is a beloved tradition. While the authenticity of the many ahaadith is debated, this event is considered a crucial part of his revelation. I think the introduction "According to Muslim traditions" perfectly suits this situation, given that the event is only recorded by Muslims.

I would be interested if anyone knows of a competing tradition, because admittedly this is not my speciality.

Also, Happy Mevlüt to y'all. '''''' smash!