Garden party challenges

Can anyone help me with the garden party challenges?
Specifically trying to get the third data disc without getting spotted. I get the first two no problem. For the third, I wait behind the pile of wood boards and wait for the guard with the disc to come over. I take him down with a stealth takedown and for some reason it alerts the guard in the rook behind me every time.

I’ve watched Mr freeze do it, and I can’t figure out what I’m doing wrong.