Team as in our OCs, who should at that time be Chunin level and assumed fairly competent.
As for keeping Azumi hidden...
Her attacks have the common thread since they're aimed at stirring conflict between the great nations, and she openly declared her challenge to them during the Chunin exams. That last part is really important.
The way I see her getting exposed is if she leaves enough clues for them to draw a link to Amegakure and that one crazy Ame kunoichi who won the Chunin exams and then challenged the 5 Great Nations. They might not immediately think it's her, but it'd probably be worth looking into and might result in her getting exposed.
I'd suggest mixing things up a bit.
Take advantage of some confusion to carry out her missions. Since there aren't really any other attacks of Azumi's nature going on it's kinda easy to link them together. She should probably work more on instigating other minor nations or just conflict in general so that her the incidents caused by her missions doesn't stand out as much.
That or she could hire mercenaries or other minor villages to harass the nations. That would also provide some cover for her attacks and she can hide her activities among the chaos.
These are the groups that would probably be willing to do business with her:
- Nadeshiko
- Depends on the nature of what she wants.
- Ishigakure
- Terrorist Group — Prime Choice
- Akatsuki
- Possibly but I'm not too sure. She could probably use their attacks as a smokescreen for her own which are less significant and more likely to be overlooked.
- Minor Mercenary Groups
- Can probably get them to do smaller attacks as distractions.
- Other Minor Villages.
- Possibly could get them to do passive-aggressive actions as a smokescreen