And perhaps (if) you decide to use the drill, do so to ony get in the rough general vacinity of the thickness you are looking for. There is value, especially if this is #1, to using the tools (gouge, planes, scapers) to take off wood for the sake of learning to use the tools. I wouldn't want to only have 1mm or so left to go when I first put (hand) tool to wood, then go too deep (it can be super surprising how quickly one gets thin) or learn whoa...when I cut "this way" things (hunks bigger than 1mm) tear out.
Good luck and have fun. It is very cool when the plate starts to sound.
John