It explains why he can 180 no scope people in a split second with a pistol at sniper range

I read somewhere years ago, I don't remember where, that if you shake it, it melts more of the ice and the drink isn't as strong.

Maybe. Given that shaking is faster one could also just assume (rightly from context) that it could simply be he is an alcoholic- or a busy alcoholic, and shaking is generally faster.
The popularly documented reason is that Ian Fleming liked his Martinis that way- so Bond did too.
Of course Fleming reportedly told his biographer he preferred shaken to stirred as it “preserved the flavor of the drink,” but most studies suggest that shaking waters the drink down and thusly dilutes the drink. That conflicts a bit to the popular notion that shaking produces a more “rough” or “harsh” drink- until one considers that stirring tends to aerate the drink which can change the flavor and Fleming may simply think the “truer” flavor of the drink is the less aerated one.