For me, up to that point when he entered that room, Brett believed that he was hunting for a small creature. However, upon further reflection, I agree with you that he acted stupidly when, after finding the shedded skin, instead of reporting his discovery to the crew, Brett decided to proceed further into the room, and placed himself in greater danger. Another moment that can be argued for a case of stupidity is when the captain went alone into the vents without a partner. So, in conclusion, I retract what I said earlier about the first movie.
Yeah Brett should have called in the others at that point but his actions were still nowhere near as dumb as playing coochy coo with a completely unknown snakelike alien entity.
Dallas was pretty foolish to go into the ducts on his own but at least he had a flame thrower.