You can do that in the changing room. That´s a room in front of the sauna where everyone who is going to a sauna changes together, but the rooms are not very large. First and foremost, these are for changing clothes and resting en route, not for more extensive care and maintenance. A good trick to save both time and some changing space is to wear swimwear under your clothes before you get to the sauna.
The time you book (eg 18:00 to 20:00) is the time you have available on board the boat. This means that changing and showering must also take place during this period. As a rule, there are bookings both immediately before and after, and you have left the boat before the booking time is over. The sauna master and skipper will let you know when it's time to change.