I've not found a way to disable the on-hover display of information. Nor a way to delay it popping up, or to have an alternative way having it pop up only when wanted or like an on/off toggle. It gets in the way some times and is frustrating to move the mouse away constantly to see information behind the pop-up hover data.
This tooltip can already be turned off at: Tools > Options > View > Directory Tree > Tooltip
TreeSize V8.0 will have increased delays before showing the hint.