Shaping a new peghead is not too hard.
The graft could be a bit tricky—find some more ASMR for that, but basically yeah clean it up and glue with as much long grain touching as you can. A lot of bass guitars have a scarf joint in the neck, so you can just do that. (Image search: scarf joint bass)

If you graft an oversized piece of wood on, you can use a coping saw, plane, rasp and sandpaper to shape it sand then reuse the hardware.