If the gin is stored in the freezer, the stem is in the freezer, the shaker is in the freezer, and the vermouth is in the refrigerator do I need to shake or stir drink at all?  Why not just put it all together in the stem and add the garnish?

Water: the drink needs to be properly, though slightly, diluted.  One might think this unnecessary since spirits already contain water.  After all 100 proof gin is basically 50% ethanol and 50% water right out of the bottle.  But that extra bit of water from the ice makes a big difference in taste.