The general feeling is that Shakespeare wasn't meaning an organ as such, rather using the term simply to mean musical instrument. There is a modern English text HERE that says little instrument, and other notes (HERE) would support this. Maybe the confusion is brought about by Hamlet referring to the recorder holes as both ventages and stops, which serves to underline the metaphorical nature of the text, which doesn't lend itself to any sort of literal clarity as Hamlet is using the recorder to make a point which isn't in the least bit musical.