In the 50s and 60s (and it may well still be the case) it was the practice in Suffolk to refer to all instruments as a Music; hence 'He yu got yu music wi yu, bo?' simply referred to an instrument, not bits of paper with dots on.
That being so, only one agent noun is required. However please note the noun is not musician, but, as Harry Cox, albeit born north of Diss, would have it - musicianer!