What you plan is fine. From Puno you have the choice of the 4M or Rutas Del Sur tourist buses. Both will take you to the town of Chivay. the Rutas Del Sur bus gets in at 12:30 and I think the 4M at 12:00..
From Chivay you would have to then take a collectivo or bus heading to Cabanaconde, where you would have to overnight. Places there are happy to store your large bags whilst you go trekking.
On your return you would have to leave the canyon very early in order to catch a bus back to Chivay and then on to Arequipa
4M would drop you off in Chivay. Then take a public bus to Cabanaconde. Any hotel there can help you plan your trek down into the canyon. Then, as Pierre already said, you can take a public bus from Cabanaconde to Arequipa. This website helped us a lot when we were planning our trek: