In the one piece shorts, depending on how/where the cup is situated, I wonder if it would get in the way of the Kinesiology wrap. Same with wearing the core shorts over your jock. Seems like you’d want the core shorts/KT wrap as close to your body as possible, and the cup/ compression shorts over top of that. That way the the KT is supporting the muscles, not being wrapped over the cup, which will deform the tension/support.