I'm not the boss, but I am good with the idea of a non-participant drawing coins (or similar) out of a hat (or burlap potato sack, crown royal bag, etc.) and matching them up to a name at the GTG.
I went back to my PM history and the group message Santa sent all the builders. He said this "We need to finalize a drawing date. This can happen anytime, but I would prefer it be announced on Christmas Eve/Christmas Day. This will build suspense and keep it fair. And, in the unfortunate situation someone cannot complete the build, we will not have to 're-draw' saws."
I like surprises, too, so if we can find an honest, salt of the earth type person, to conduct the drawing in private, and post a video link on Christmas Eve or Christmas morning, that would be cool, too.
I will agree shipping should take place after January 1 to miss the holiday rush and reduce the odds of lost/damaged/stolen shipments.