I do not know of a salt water bath in the Vaud area, but there are two thermal spring baths there: Lavey-les-Bains , and Yverdon-les-Bains . And one across the lake in Evian .
BernAqua in Westside has some other kind of special filters to clean the water. I've been there several times and never smelled any chlorine. I'm not clear tho if chlorine is actually used or not:
Well I am must say that my experience with the lake was not a tempting one...we got itchy from the swim and had a wonderful encounter with unattractive rubbish
Maybe what you are looking for are swimming pools with ultra violet disinfection. There might be this kind of system in switzerland, I used to go to a swimming pool with this system, that's why I know about it, but it was back home.
Salt water pools are set up so that as the water is filtered, it runs through a series of electrical plates which convert the sodium chloride to free chlorine. This means that the pool actually does have chlorine in it (it makes it's own) but it's usually at a lower concentration than one that just gets raw chlorine dumped in.
Chlorine added to fresh water is more effective and cheaper to maintain than a saltwater system, so usually public pools are going to to be chlorinated with either gas, liquid or powdered chlorine. In any case, they will have tons more chlorine than a residential pool.
(maybe too much info, but I used to own a pool service company)