So... While pp are right that a deodorant won't stop you actually sweating, they are wrong that all they can do is mask the smell. This is certainly true if all that is used is nothing but a scented product. However, there are some absolutely fantastic all-natural products that have ingredients in them that are actually very effective.
Get one that is based on coconut oil. This will go on easily, and will moisturise under the arms. Coconut oil is antibacterial and antifungal, which will help prevent sweat starting to smell bad. Additionally, both bicarbonate of soda and arrowroot powder will absorb moisture and neutralise odours. So yes, people will still sweat (our bodies are supposed to do this!), but sweat doesn't need to smell bad if you cleanse regularly and use a deodorant product that prevents bacteria etc. Any essential oils added to the product will smell nice, and some (like lavender) are powerfully antibacterial too.
I've been using natural products for ten years. The best I've tried so far are both the brand called Humble, and another called Your Nature Life (I think!... Sorry, I'm out of the house just now). I'm using the latter currently. It's over 30 degrees here and I've been very busy today. No smell at all! And no, I'm not immune to it....I definitely know when I'm wiffy, as I've been able to smell myself after some other products I've tried that don't contain the above ingredients.
Just to add though, I don't sweat huge amounts under the arms. I sweat more on my face and neck. I need an antiperspirant there!