Exchange2013 Hybrid to OnLine only, but keeping ADFS and DirSync ?

We have Exchange2013 on premises (Virtual), and we have a hybrid config, all mailboxes have been moved to the cloud, and the MX records point to the Exchange Online.

we have a small number of devices that need email services (printers etc)

we use ADFS on another server for authentication with MS services such as CRM

we have DirSync installed for password/AD synchronising one way to EOL.

we want to remove the Exchange2013 server as a redundant unit.

We need to keep using ADFS, and I'd like to keep using DirSync for password sync.

Reading this, scenario 2 looks relevant, it says that we need to keep Exchange on premises?

https://technet.microsoft.com/en-us/library/dn931280%28v=exchg.150%29.aspx?f=255&MSPPError=-2147217396

Can we get rid of Exchange and keep ADFS and DirSync?

if not, is Exchange2016 a better solution?

do we need to upgrade to the new Azure AD Connect?

https://azure.microsoft.com/en-gb/documentation/articles/active-directory-aadconnect-dirsync-upgrade-get-started/

I want to reduce the resources needed, as much as possible, and preferably, get rid of Exchange on premises

all thoughts and advice welcome

thanks

G