Just tell them you can’t swim. If you decide USNA is the path for you, then I would highly recommend swim lessons during the application process. It’s a great workout and life long skill. It will also make swim class much easier at USNA and one thing you don’t have to stress about.
^ This ! You don't need to be able to swim to attend USNA, but being comfortable in the water is a life skill that may save your life someday. First, even if you "tell them you can't swim", "they" may make you prove it. I recall one of my NAPS classmates telling the training staff that he couldn't swim, but they made him do the tower jump anyway, and picked him off the bottom of the pool. (Classmate was a a roommate for a year at NAPS before he got ac boarded out, and to this day I think that was one of the bravest things I've ever seen -- jumping into a pool knowing you cant swim). He was put on sub-squad and learned to swim before NAPS was done.
You don't have to be a great swimmer....but most of what you do in the Navy will be in and around water. I live near the Mississippi River, and so many people drown unnecessarily because they fall in, can't swim. You don't have to be a great swimmer, you just need to be able to get yourself to safety.
Finally, if you have dreams of flying, alot of preliminary Aviation Indoctrination involves swimming. It's like some mad scientist comes up with ways to torture people in the water. The Single seat dunker (watch Officer and Gentleman), parachute drags, and my favorite , the help (or multi -seat) dunker. Being comfortable in the water makes life alot easier.
I was fortunate, I was a swimmer when I was young ...so all this was easy. USNA recognizes that not everyone has that background, so swimming is a major part of the physical ed program. If you are a swimmer, you can validate (and as a Plebe, that extra 2-3 free hours a week was welcome !) But if you aren't a swimmer...Navy will teach you.