Choose from the damage types you are using. It's the solution that interpolates the least in the way of additional rules into applying the ability.I don't know what basis there would be for making it radiant or necrotic if they weren't there already. It would probably just come out and say "add your proficiency bonus in radiant or necrotic damage" if that was the case.
If it were Hunter's Mark, where it is specifically for a weapon attack I'd say the basic weapon damage logically should determine the spell damage type, even if the weapon had some sort of other damage rider, was used with Booming Blade, etc. But there is no consistent basis for what the "core" damage is with all things that trigger Hexblade's Curse damage. It's not just weapon attack damage, it's whenever you're rolling damage against them. So it seems like the choices are "interpolate in a bunch of assumptions about how it was supposed to work" or just let the player pick which damage die (and hence which damage type) they are attaching their proficiency bonus to.
ncG1vNJzZmivp6x7prrWqKmlnF6kv6h706GpnpmUqHypsdebo5qclWKwtr7SnmSdmZ2WtKZ5wailrqtdrLa1tIymrKWsmaW5pnnDmqSan5Viwbq8xKxlb29jbIF3ew%3D%3D