Perhaps with an application which can manipulate windows and play pre-defined keystrokes etc. like
Hot Keyboard, BSPlayer-window could (by a predefined "hot-key") first be made active window - followed by BSPlayer's instruction - followed by restoring previous active window? Perhaps not really global keys (but aren't global keys usually applicable only within one application or within a suite of related applications?) but the result would pretty much be what is intended? Don't know if it could work.