Can I just shut down the last Exchange server in a hybrid setup?

Shutting the server down and fully removing Exchange are different choices. If you still need to manage synchronized recipients, plan how you’ll manage them before taking away the server you use for that work. A management-tools-only machine is one option. If you’re ending the hybrid arrangement entirely, follow the relevant decommission procedure rather than treating a shutdown as the whole process.

Removing the management tools should not itself erase Exchange attributes from Active Directory. They’re management software, not the data store. The bigger question is whether you’ll have a safe, supported way to change those attributes afterward. Direct edits in the attribute editor can be error-prone, and not every Exchange-related attribute is handled like an ordinary directory field.

If the goal is to stop running the server but keep directory sync, look at the management-tools-only approach and confirm it covers the recipient changes your team actually makes. That gives you Exchange-specific commands without keeping the full server role. Don’t assume every group or recipient task has the same requirements, though. Test the routine changes you depend on before switching over.

There may also be cloud-side management for some synchronized remote mailbox attributes, but don’t assume it replaces every on-prem management task. Check which attributes and recipient types it covers in your setup. If you remove the last server and the tools without checking that first, you could find later that a change you used to make has no workable path.