I think you're right about Tessio. He was a traitor but unlike, say, Carlo or Moe Green, we didn't see him overtly doing violence or disrespecting Michael. So, I'm guessing, FFC believed that it would be somewhat jarring to show his actual, violent death on screen. Besides, there was plenty enough death in that scene.
Some people here have guessed that Tessio was "taken for a ride" and shot, quick and neat, in some deserted place, probably dumped there. Garroting would have been too prolonged and painful for him--note that even at the end, Cicci treats him with respect: "Excuse me, Sal...."
Good point TB. Garroting is a bit less respectful than being executed by a gun. I imagine he took two shots to the head, got a pair of cement boots and slept with the fishes in the East River.
