Hi John,
You will basically need to keep ADFS and DirSync in place. However, you can fully decommission your Exchange 2010 environment. Because the Exchange 2010 attributes remain in your local AD, you can still run the EMC and connect directly to Office 365 to manage your accounts.
Most of the time the reason for most organizations that have configured a hybrid deployment, removing the last Exchange server from the on-premises environment will have adverse effects. In most cases, we recommend that you leave at least one Exchange 2010 Server on-premises for mailbox management unless you are getting rid of the on-premises messaging and identity management dependencies all together.
More details, see Decommissioning your Exchange 2010 servers in a Hybrid Deployment.
http://blogs.technet.com/b/exchange/archive/2012/12/05/decommissioning-your-exchange-2010-servers-in-a-hybrid-deployment.aspx
Thanks,
Monica Tong