The previous post discussed why a world-wide military needs to be limited to preventing warfare or the use of military threats. This is a disadvantage of a military compared to using strategic non-violence.
A non-violent brigade under the command of a legally constituted world body, such as the United Nations, could be authorized to enforce legal policy decisions of world governing institutions. To use the examples given, we can imagine some kind of non-violent brigade entering a country to inform people of a world-wide ban on genital mutilation, and use some method to enforce that ban.
Likewise, a non-violent brigade could be used to pressure a country to stop polluting.
These uses of strategic non-violence would not be defeating the purpose of non-violence replacing warfare. They would in fact be strengthening that purpose.