There isn't a button per say however, you can set the time delay it begins transmitting. So, ex. you briefly cough it doesn't immediately broadcast it. With that said, I haven't really played around with that feature to be completely honest, so I can't give you any realistic feedback. I use the default settings the ROM/FX came with and really don't have any problems, and yes I cough and make other natural noises without complaints from others around me.
With my TD and HWT set ups I've been toying around with the idea of using a micro switch to interrupt my TK chatter chatter so I can speak without being interrupted. My plan is to use a micro pressure or magnetic switch but this is still in the development stages.