Hmm... the waters here are very muddy
I use a CNC machine to create all manner of 'things' - look back over some of my posts this year and you'll see the 'Giraffe' Clock and the 'Siamese Cat' box to mention just a couple. These were designed and made 'by hand' - ie. 'created' from my own thought processes and transfered to a finished article by me personally selecting suitable materials and processing them 'by hand', albeit with the aid of Power Saw, Pillar Drill, Milling Machine, Lathe, Router, Gear Hobber, CNC, Linisher . . . . etc.
I've no idea how you go about making or repairing clocks (never mind Watches!) but you may well have a Pinion Mill - would the use of such mean that the resulting clock could not be called 'Hand Made' ?
Programming a CNC machine is not a soul-less machine activity, it has to start with a drawing which will have come from some form of creative inspiration. It may then require 'adjustment' - often by hand or eye - to achieve the final desired effect.
As I said at the start - the waters are 'muddy'.