I took the best of Switzerland tour this year but went in late May, early June so no swimming. To wet any rainy!! However, there is sports center in Murrin and one of our tour members went there for a massage and they have a pool. The hotel there actually had sauna and the hotel in Engelberg also had a sauna. You can certainly make time to use the pools and saunas as all stops have free time. I did not because there were so many other things to do.
I have also gone on the GAS tour and went to the Frederiksberg (naked) spa in Baden Baden and while it was way out of my comfort zone, I would not have missed it for the world and it was one of the highlights of the trip. They also have another spa where there are outside pools and and several of the tour members went there.
If you think you may swim, pack a suit. As the other poster has said it does not take up much room. Or, you can buy one there and have it as a souvenir of your trip.