I'm going to joke around with my friend with this new guy.
Why are you going to joke about them?
Because I know that they're not going to get offended.
Joking around with your friends is great as long as you aren't being mean. If your friend and the new guy think your jokes are funny then there's no problem. But if they don't like what you're saying then you should stop.
But I find it funny to see how thin skinned my friend is and how the new guy is getting flustered by the situation.
You see that is wrong to do. You shouldn't  joke to see how thin skinned your friends are. They will resent you for it.