override the default cursor

In a Qt application, is there an equivalent to QApplication::setFont that sets the applications default cursor, to be overwritten by setting one on a specific widget?

QApplication::setOverrideCursor overrides all widget specific ones, I want local ones to take precedence over this one, but still use my cursor if I didn't specify one.

QWidget::cursor?

I'm trying to avoid having to go around to everywhere I construct a widget and add that in. This is required by a recent change, and if we get a different cursor we want to use, going through the entire app to change it would be a pain. I was expecting that given that there was a way to do this for fonts there would be a way to do it for cursors?