You won't "have to strip off with everyone else."Please excuse me if my previous post was misleading. I just happened to be in a special situation (a backstage room, to be precise) but still we covered ourselves with the big kimono as we undressed ourselves, so that no one had to see our aging bodies!
But usually, you will be the only person in the room when you take off your bra to change into the hadajuban. Then typically the clerk will ask from the other side of the door or curtain to see if you're done, and if you are they will come in and see you all dressed in the Japanese undergarments as shown in the link I posted previously. They might adjust these undergarments a little, but professionals do it so well that they will never see any part of your body you don't show at a swimming pool.
Needless to say, the dressers are always females and these undergarments are as thick as T-shirts that you can't see through. But do be sure to take off your bra, because it will really get in your way as the big obi belt comes right under your breasts. In other words, the obi will secure your breasts therefore not requiring any bras.
Don't worry about it. It will be a splendid experience, I am sure.