The commissioner can suspend the draft clock at any time. He can run the whole thing manually.
He can also draft for any team, so you don't really need one PC per team unless everyone wants to have their pre-ranks loaded into the draft room.
I think it would be OK to have three computers -- 'in the hole' and 'on deck' PCs set up for researching as a pick approaches, and the commish computer for actually making the pick, supervised by the commish. The commish computer hooked up to a projector or TV for all to see would be cool too.
The draft room is pretty flexible. Your commish should go in there and mess around to see what is possible.
Be excellent to each other.