There is a difference between a "cleaner" and a "disinfectant". Caustic based chemicals are generally considered cleaners meaning they remove soils from the surface. They are not considered disinfectants. On the acids front, it depends on the type of acid and the concentration. Some acid based chemicals can be disinfectants.
I understand your concern with the chlorine and stainless as chlorine can pit stainless steel. However, low levels of chlorine as a one time or periodic disinfectant in your water system will not be an issue. Chlorine pitting stainless typically happens when it is used regularly at higher concentrations, like supplemental cleaners during cleaning of equipment. For example, in our facility our main cleaner contains chlorine around 150 to 300 PPM and we circulate it at temperature, about 150 degrees, for 15 minutes to an hour on stainless steel equipment. We do not see pitting in our equipment from it. Now, if the chlorine was sitting on the surface for a length period of time, then you start running into pitting problems.
I would recommend you consult your chemical supplier and get their recommendations.