Well there really aren't any sports that aren't athletic......
Maybe you should try to become athletic because the there are sooo many sports that you can benifit from!!! Here are some ideas
cheerleading: I do this sport and love it! It is sooo much fun to hang out with your friends!
swim club: Hanging by the pool is always fun!
soccer club: Hard, but very fun because you can be competitive
Pom squad: Lots of dancing and chanting!!!
Hope some of my ideas intriged you!
Yeah, swimming is really cool but it wouldn't hurt to try table tennis as well :). Just saying, because i do play it actively and i love it. Not only does it improve your overall fitness but it exercises your brain as well which is pretty cool if you ask me.
In the beginning you might not even break a sweat but later as your game gets better and better, you will be excessively sweating and getting in shape.
But , thats just me. What i am trying to say is to try as many sports as you can, until you find one that you absolutely love and are good at. I tried many sports, soccer, basketball, judo, but i just had no passion for them. Not until i was introduced to table tennis. Now, i look forward to every training session and just can't wait for tournaments.
In conclusion, if swimming sounds great, go for it and see how it goes. If it doesn't go great, there's always some other sport for you to try.
Have a nice day!