Are you arriving at Narita? Then, just use one of the currency exchange booths at the Narita Airport upon your arrival. That's what I always do. You'll probably get better rates there than in Italy.
Then, one less thing to worry about.
I got some older bills in my wallet as I only visit once a year or so. Never got a problem. If you are concerned with older currencies you already have, you can always stop by at any bank and ask them to either check or change them.