I think Shunsui handles her pretty well but that probably has a lot to do with him being one of Old Man Yama's original disciples.It's been foreshadowed the entire series, every member of the Gotei 13 aside from the head Captain has displayed fear of Unohana. Every single one freaks out if she's even irritated and they don't even know the history. She's got a menacing air under that constant smile.
Kinda breaks my heart watching Shunsui try to hold it together while everybody else is in a panic.