why bother? No one really cares in bath houses. I know in Japanese bath houses many older men, not gay, would compare erection sizes and most importantly, how uncover the glans are. They'll even wash younger guy's penis and help them stay uncover with tips. It's of most important to Japanese men to appear uncovered because it means being an adult. It's natural and they don't think they are gay; they would do this to their own sons when they reach around 10 to 12 years of age. Erections w/o head being covered is not shameful. No need to hide it in places like bath houses.
Fun fact: In ancient Japan, most people are not shameful of nudity or sexuality. Penis are often objects of worship. Many rural villages have special places staffed by older women, whose only purpose was to help male teenagers. A Japanese men MUST appear to be pulledback in public to be considered a real man, and with public baths everyone can see everyone else's state of exposure. If you appear before another adult, man or woman, with glans covered, you are considered either an immature child, or someone who has sinister intentions. Glans must be exposed to show honesty and purity.
So when a teen reached puberty and the glans are still covered, the parents worry and would try to help. Often the parents do not do a good job, so they send these kids to special places in the village, where there are older women who does nothing but to massage the penis and to pull the skin back. They use special massage and oral techniques to increase the length of the penis and the size of the glans itself, because that's the best way to help the penis stay permanently exposed. The goal is to have the glans at LEAST only half covered when soft, but most be completely out during erection. These are not considered sex shops as they will not bring the boys to orgasm - the point is to be exposed and remain semi-hard as long as possible.
These place are rare now so must guys rely on friends and family to help them do the pull back. Some mothers start the boys on "skin pull back exercises" as young as 3 years old. By middle school almost all boys can retract and attempt to stay exposed all the time, a state called "zuru muke". Many were successful. A few friend of mine did this and now they are barely covered when soft. They usually pull it back fully in baths. One told me about these special places in the rural villages because he went through one himself... he said his penis grew to about 18 cm and mushroom like head, and his skin never touched the glans - always look like he's completely cut. From what I can tell he's correct. He has the biggest head I've ever seen, which also inspired me to stay pulled back now.
I did ask him how they manage to get his head this big, he said there are secret technique to this. They basically force him to stay pulled back all the time, giving him special underware which force the head out 24 x 7. He cannot masturbate during the process. When they gave him treatment, they would press on some acupuncture points around the penis to force full erection from him, and massage the shaft to help the head engorge with blood. Kind of similar to jelqing I think. The difference is, the women would women would hold the glans in their mouth and use the tongue to tease the urethra. Its not a blow job since there's no movement, the mouth is there to increase the temperature of the glans to help it expand. The teasing was done to increase the blood flow and the opening of energy points at the spot. Once they reach their max size they slow down until he was ready to blow, then they stop and press his shaft to stop the orgasmic response. Once he calmed down they would continue, until he is at max size again, then porlong the sexual highten feeling as long as possible until he's ready to shoot again. They would repeat this process for an hour, then leave him w/o orgasm. The penis would stay hard for hours after this. In the mean time, he cannot come by himself. Once a week he's allowed to come in front of them, but he had to do it himself while they observe his technique. Even masturbation as taught to ensure growth and glan exposure. After a year or two of this treatment, his penis reached 18 cm when erect from his previous size of 11 cm. He said it's the best experience of his life, having these women teaching him how to be pulled back and possessing a large penis. He shows it off anytime he can, and is the most confident man I know. I really wish I had help like that.
If you don't get what I am talking about, go watch the movie "In the realm of Senses", a movie about Japan of 100 years ago with uncensored sex scenes. It's a shocking movie but if you pay attention, you'll find that every single penis there is uncovered, hard or soft. The main character's penis is completely uncovered all the time, and dark all over. This is a trained penis. Go watch it and you'll see how these people who never practiced circumcision, all look so cut in the ancient days.