Asonero Are you sure the distance is as large as 10px? I haven't checked but editor controls should be using the same distance and it appears to be smaller. In fact Godot may be using OS gui settings for drag/drop sensitivity.
Anyway, I'm not aware of a way to affect it directly from Godot, but you can use force_drag() instead of _get_drag_data() to start the drag whenever you want. Just track what the mouse is doing via control's _gui_input() and then call force_drag() when conditions are met.