So, you set the poisonous creature free and now you should get past Cletus undetected.
There is a laser pointer in the creature's luggage. Grab it.
From the back position (among the luggages, that is), point the laser pointer to the pipe. You get a skippable minigame.
Now Cletus is in better position to steal his ID card. Go to the pipe (just click it) and steal the ID. Did you push the call button?
It makes too much noise and Cletus spots it.
Maybe you could make some noise to the tubes. Wasn't McCormick down there? Talk to him.
Now, he is in the tubes and poisoned by the creature.
Good idea! Give him the antidote. Now the tubes are filled with... umm.. noises.
Please, don't. Okay, go up and push the call button. The slot is open now. Insert Cletus' ID card into the slot.