You can do this with your friends. You can do this with your nose. But don't do it with your friend's nose!

“Touch”

While you can touch your friends and your nose, the phrase 'don't do it with your friend's nose' does not logically fit with touching.

“Smell”

You can smell with your nose and perhaps with friends in a group setting, but it doesn't work with the context of 'don't do it with your friend's nose'.

“Laugh”

Laughing can be shared with friends and is often associated with fun, but it doesn't connect to the idea of 'doing it with your nose'.