If the lesser sex is attending your baby shower, serve notice they're on foreign territory by playing the 'dunce hat' baby shower gag game.
The party emcee asks each gender to choose the four smartest candidates for the 'Great Baby Trivia Challenge' or whatever grandiose name which tickles your fancy. Once players are chosen, announce the losing contestants will be required to wear a dunce hat!
Here's where the game gets fun. Have the emcee ask loaded questions where the men have no chance of getting the correct answer. Ask a question like 'what will be the baby's preferred type of baby food?' The man might guess apple sauce, the lady contestant might guess spinach. And the correct answer is... spinach!
Once a contestant has guessed 3 questions incorrectly, they are given a dunce hat to wear throughout the remainder of the shower. Keep playing until all your male contestants are certified losers!
A variation for the office party
Everyone likes to pick on upper level management! For those throwing an office baby shower, have 4 male big wigs and a beloved female coworker play the game. One will win and 4 will lose... you can guess who!