Tessio was simply slippin' as his Don was. He did not believe in michael and just got desparate. The main point is that he chose to betray. How he did it is trivia. Tessio being a capo-regime would have arranged for dozens of murders(like the maranzano one). But he was not unique in that. Even Clemenza must have had experience in sneakily killing people. But his good fortune, he chose to stay loyal to michael