Trying to put neo-noir back into the 50s is unworkable, because there's just not enough of it. M by C doesn't reallty look ahead to a new style, it slyly parodies the old one--or, perhaps more accurately, sends up the psycho hit man film or that character type that's emergent in the 50s. In its unique little way, it's a culmination of something in an analogous way that TOUCH OF EVIL is (on a more grandiose scale, of course).
Siegel's THE KILLERS (1964) is pushing toward neo-noir because it makes the villains into the investigators--it changes up a long-standing noir convention that compels us to strictly separate the good guts from the bad guts. It's a relativism that doesn't exist previously in noir's storytelling mode (though it starts to show up in the 50s in particular variants of "bad cop" noirs such as BIG COMBO (Cornel Wilde) or (in France) RAFLES SUR LA VILLE (Michel Piccoli). There is a lot more of this uncertainty/randomness floating around in neo-noir characters, going beyond the charismatic villain that initially animates early noir (think Gabin).