2 or 3 years ago we set off from Montreux for a day trip to an outdoor mountain pool and cafe (seem to remember it had some wildlife too) but we got sidetracked and never made it.
I've got visitors coming in early Sept and it's the sort of thing they'd love but I can't find any reference to the place anywhere nor recall exactly where it is/what it's called.
Not sure about the wildlife - but near Montreux you have the Bains de Lavey, or the Bains de Val d'Illiez- or for up the mountains with great views, the Bains d'Ovronnaz. Or going north, the Bains de Charmey (which you can do after a great visit to Gruyères village).