By the time you're doing that, you're not feeling it as the spotlight is on you. You should feel connected with the person you're playing against and you should just flow. The people there in the pictures you see are probably appreciating the creativity of the players, set as a foil to the art as a whole.
Saying that you don't think you can do it because you would be embarrassed makes you look really ridiculous. You're basically giving up on yourself because you can't put yourself outside your area of comfort. You might as well say that you'd LIKE to learn how to do flips, but don't wanna go through the effort if you fall down and have to get back up again.
I just wanted to point that out, but anyway, just deal with it when or if the time comes.
That girl you know in gymastics is one girl. She could have her medals from doing events like bars, balance beam, or pommel horse (which, in my opinion, aside from the rings, is the most impressive), when the skills that you want come from that freestyle stuff that they do on the mat.
Anyway, check those things out if you can, the more you talk to the instuctors the more info you'll get. The more info you get, the more options you get. Don't have your sights set on only one thing, because things become a factor like location, price, instruction quality, etc.
You could be at the best wushu place is aussieland, but if they just focus on weapons and sparring tournaments, then you're not going to get what you really want.
Have your goals in mind when you talk to the school's people, discuss, learn, etc. But try to have a good idea of what you're looking for in the particular style when you go...for instance, if you go talk to gymnastics schools, ask them if you can choose the things you want, like if you don't wanna do bars, your focus could be somewhere else. Or if you go to a martial arts school, find out what they focus on, etc.