As to the OP, I think you should wear what you want. It's a parade with military significance. The white shirt will distinguish you as Navy, and your ribbons and badges are appropriate. I have worn mine with a khaki shirt to good effect. I like to see them on those who have them as they are not items of military uniform; they are personal awards and decorations, so they are fine to wear on civilian clothes.

I would not wear any uniform item with insignia, etc. that are decidedly an item of military uniform for anything other than a parade. (Personally, I wouldn't even wear anything besides a cover for a parade, but if others do, it's fine with me.) My khaki shirts have no chevrons or USMC badges, they're just khaki shirts. I am not in the military now, and even though I am still a Marine, I am no longer a sergeant! (Much younger, better looking, and more capable men are doing that stuff now.)

I hope to see a photo when you decide for sure.

Thank you for your service.