Kasumi has been running away for so much time she is basically a hide and seek specialist. Ayane is from the side of the village that is specialized in staying in the dark and doing unseen stuff, and Ryu is just better at everything. So, Hayate would be my pick for first catch.
Hayabusa. The Mugen Tenshin Ninjas tend to be more secretive and prefer to do their tasks in the shadows. Hayabusa is like 'screw stealth just charge in' so he his skill in hiding would not be as great as the Mugen Tenshin Ninjas.