I also like to avoid the vapors of chlorine in water, etc.
So I don’t bath but make vapor bath instead:
My trick is to use clean water for the boiling water and for the sitz bath.
The water for the sitz bath has been outside overnight and it is real cold.
I have reverse osmosis system at home which brings 700 ppm (parts per million -the water here where I live is full of lime) to 40 ppm and then a devise to clean/energise it a bit more. That I think is good enough for this purpose.
The second trick is that I use an electric stove under the boiling water pot, so in aprox. 18 minutes I'm sweating.