I don't quite follow. Why will there be nothing structural left? a 16mm dowel should be a tight fit. It will be bored to 14mm, then tapped to M16.Drill down with your larger bit untill you hit the nail. Then use your carbide burr to remove the nail, leaving as much wood untouched as you can. Then finish drilling your larger hole.
For the larger hole I'd suggest going quite a bit larger than 16mm. If you fit a 16mm dowel you will have nothing structural left to take the M16 thread. I'd go 20mm at least or 25mm if you hafe the room. A std brush shaft is 25mm & will give you a good hardwood dowel.