Hello, @@Jamie McFarling,
Welcome to the Microsoft Q&A platform!
Traditionally, maintaining an on-premises Exchange server is recommended for hybrid configurations, especially with Azure AD Connect for directory synchronization. However, you can fully migrate to Exchange Online while retaining Azure AD Connect for directory synchronization. You can consider options like Azure AD Connect Cloud Sync, a lightweight agent that synchronizes your on-premises Active Directory with Azure AD but doesn't support writeback to on-premises.
(Relevant issue: Azure AD Connect cloud sync and Exchange Online only? - Microsoft Q&A)
Third-party tools can manage Exchange attributes without an on-premises server, or you could manually manage these attributes using tools like ADSI Edit or PowerShell scripts.
Once your mailboxes are fully migrated, you can decommission the last Exchange server by converting on-premises mailboxes to mail-enabled users in Active Directory. This process will lose some GUI management tools, but you can manage necessary attributes using PowerShell or third-party tools.
Should you need more help on this, you can feel free to post back.
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Thank you for your support and understanding.
Best Wishes,
Alex Zhang