Laughing at a joke you didn’t get just means you’ll miss the next one too.

The fake laugh is a tiny vote for looking fine over knowing what is going on, and it repeats. Once you have laughed, asking gets harder, and the next reference lands on the same gap, so you spend the whole conversation half a step behind everyone else. The cost of that is not embarrassment. It is being slowly outside something you are physically inside.

Try the honest version once. Say you missed it and ask them to explain. People almost always enjoy explaining their own joke, and the second telling is usually funnier than the first anyway.