Pads are primitives, so I don't think there's any way to carve them up.
Does the hole intersect the edge?
If not, you can simply set the pad size to a minimum and then draw the pad shape as a polygon with mask expansion enabled. Unmasked polygons with a pad in the middle to establish electrical connection to the schematic symbol are the way you get arbitrary pad shapes in Altium anyway.
If so, and you don't need it plated, you could just draw the pad shape as a polygon and make the part circle of the drill part of the board outline. If you need it plated, you could either ignore the error and call out your intentions to the PCB fab, or draw the polygon and tell the fab they need to edge plate the appropriate area.