The simplest thing is probably to make sure your WSUS server is synchronizing updates for Server 2003 with the Critical or Security classification.
TechNet has articles on exporting and importing updates from other WSUS servers, and I recently fixed my report for the WanaCry updates on THWACK: UPDATED - Computer Update Status - WanaCrypt (MS17-010) - v2
I don't think MS made them available via syncing to WSUS. You have to manually import them from the Microsoft Update Catalog page using the WSUS console.
2 of 2 people found this helpful
Go to the Patch Manager server that you have WSUS installed on. Run the WSUS console,not the PM console. On the right side under Actions click on "Import Updates". This will take you to the Microsoft Update Catalog page.
Once at the Microsoft Update Catalog page enter the KB article for the 2003/XP patch, 4012598 and click Search. Select the patches you need by clicking on the Add button to the right. Once finished selecting choose View Basket at the top right of the menu.
Make sure the box is checked for "Import directly into Windows Server Update Serivces" and click on the Import button.
Once complete the patches will show up in WSUS just as if they had synced with the Windows Update servers and you can approve them for deployment.