There are no 'harsh' chemicals in UK or EU Cosmetics.
It might be useful to just clarify an important distinction. In the UK, we are regulated by the Cosmetic Regulation (EC) No 1223/2009, there is a clear distinction here between what is a cosmetic and what is a medicine. A cosmetic is defined as (I'm summarising here) 'any substance or mixture intended to be placed in contact with the external parts of the body to clean, perfume, protect and/or correct body odours.' However, any product that 'restores, corrects or modifies physiological functions' is a medicine and is regulated by the MHRA (Medicines and Healthcare Products Regulatory Authority). As cosmetic chemists, we can only produce products that fit in to the first definition.
Sweat is secreted through the Eccrine and Apocrine sweat glands in the skin. However, it is only the Apocrine sweat that releases a thicker secretion containing molecules that are broken down by our skin bacteria and cause body odour. These glands are mainly found under the armpits and in the groin area.
The term 'Harsh Chemicals' is rather emotive language based largely on misinformation. If cosmetics or personal care products were harsh on the skin, they simply will not sell. Every product has to go through various complex processes to determine their safety, including a Toxicologist's report. In my opinion, the most successful, safe and proven cosmetic active to counter Apocrine sweat is Aluminium Chlorohydrate. The Aluminium salts form a gel like structure on the skin, blocking the pore. They sit on the skin, are designed to go no further and are simply washed off the next time we bath/shower.