As far as I am concerned, you can shake any cocktail, my only concern is what
the resultant cocktail will taste like. As for speed, the quickest is just to
build everything into the glass it will be served in.
I stir a Martini/ Manhattan as there is only spirit and vermouth in them both,
there is no cream, juice etc. Stirring stops the ice from being smashed to
pieces, which is what happens when you shake a cocktail.
If you are going to shake a Martini or Manhattan, then make sure than you
strain the drink through a tea-strainer into the serving glass (this is
sometimes referred to as "double straining"). Double-straining will prevent
chips of ice from floating on the drink's surface, this ice will melt quickly
and leave a layer of water on top of the cocktail.
Cheers!
George S.
"You have your way. I have my way. As for the right way, the correct way, and
the only way, it does not exist." - F. Nietzsche
"innovation distinguishes between a leader and a follower" - Steve Jobs