G'day Jerry,The same reasoning that you apply to singing songs also applies to playing music. I always like to internalise something - song or tune - before I sing or play. Songs (and singing style) have always been memorised in the privacy of my car, which does lead to some odd looks in summer, when I forget the window is rolled down at the traffic lights! Books are invaluable resources to broaden the repertoire, not for anything more than a generalised 'prompt' when singing in public.
I also spend an inordinate time analysing tunes and working out the intricacies of extracting the full harmonies from the quirky layout of button accordion or Anglo concertins ... then ignore it once I'm actually playing! I also love good sessions ... winging it on my hearing of some other player playing tunes I may never have heard before.
All these approaches are in some measure contradictory ... yet also complementary. In the long run, you have to work with techniques that get you in and singing ... or playing ... but you are not really performing / entertaining / witnessing until you do it face to face with your audience, without words or dits getting in the way.
Regards,
Bob Bolton