Hi, basically everything is shut down in any Italian city on May 1st. Shops are 100% closed.
There are some exceptions, notably big museums (for example pinacoteca di brera or triennale di milano), which decide whether to keep open or not in the last days of April or pubs and restaurants in the Naviglio zone, which are open anyway.
My advice is to keep an eye on some portal with local events, checking what's live on May 1st (example http://milano.virgilio.it/eventi ) and make provision for a couple of alternatives for the night (example http://www.slevart.com/milan-travel-guide/milan-nightlife/)