Was thinking about this today while at work a little bit.
Not only is Strykervet probably right about mission specific gear (I say probably because I have no experience in the military at all, let alone Vietnam, so I can't confirm it, but I definitely agree with it.), but that's what I would probably want to do, if it was an option.
Unless the job at hand called for something different, I'd probably carry, as a general rule either an FAL, AK, or an M16, and either a 1911, or Browning Hi-Power.
Then I started thinking about "secret" part of a "secret mission" and decided that there were two alternative routes:
CZ-52 and a PPSHA. They both shoot 7.62 Tokarev, which I understand to be one of the rounds commonly carried by the VC, so it wouldn't leave behind any especially distinctive shell casings.
Another option (not to make light of the topic) would be to choose firearms in the most oddball calibers you could think of, so as to leave anyone who came across the shell casings confused. Maybe 9mm Largo and that .260 Remington Fireball that the AR was originally supposed to be in....