Agree with prior two comments. The games mentioned feature it and it is expected. It isn't an underlying premise of CoC, and subverted expectations are often hard sells for gamers who have a limited time to game.
Look here I am! I do get an e-mail message when I'm tagged in Yog-Sothoth.
My emphasis on the zoog was on tricks and traps rather than weapons because how can they be warriors, really? I don't think they have a "warrior" class in their populace or an "army", so no real tradition of weapons, though obviously they can use whatever.
I'd argue that typically they would use bite and claw attacks, augmented with whatever weapons your game has which are suitable for a tiny creature. Darts, daggers, spears, perhaps small bows. Any kind of weapon that works by exerting strength like a club seems like it would be out.
PC betrayal absolutely requires player buy-in at the start for a game like Call of Cthulhu, in which the odds are already against the players without one of their number back-stabbing them. Unlike in Paranoia, Skullduggery, and Fiasco, where treachery is baked into the premise, its potential to blow up in people's faces in CoC outweighs the possible dramatic "surprise twist" later in the campaign.
If players do like the idea, there are rules mechanics that can incorporate the theme into game play, such as Bonds in Delta Green for CoC or the Trust/Betrayal rules from Night's Black Agents for Trail of Cthulhu.