You COULD do a modified version and zip of the jacket to just above the shorts. Make the shorts longer. Wear a plain shirt or tank top and just not unzip the jacket unless you're resting. No one will get on you for "being inaccurate" (and if they do, they're butts and don't listen to them lol). People modify outfits ALL THE TIME because it just makes them feel more comfortable.
At the end it's up to you and how comfortable you feel with it. If you're uncomfortable, it will show. And then it's kinda up to your parents, unless you want to sneak it, but that's a whole different story.
Here's a pic of kinda what I'm talking about. Sorry for it being so awful lmao:
You'll just have to emphasize that you WILL be wearing a shirt or tank top underneath. And not a bikini at all. And then when you get older, you can always redux it (if it stills fits you and you don't grow too much xD)