When are Bone Charms found during a mission determined?
In general, you won't have much luck scumming.
According to the Dishonored wiki,
Charms spawn randomly. They are chosen when the level is loaded so reloading right before obtaining one will always yeild the same charm.
However, there are at least two charms that are scummable. The first, in the vice behind the High Overseer's Office, is determined when the vice is opened. The second is the one in Daud's pouch. I've tried both of these and confirmed them.