I found that this was possible after further digging:

https://ccm.net/faq/25198-word-extract-all-hyperlinks-from-a-document

I found that this was possible after further digging:

1. Press Alt + F9 to display the fields
2. Ctrl + F to open the search box
3. Search: ^d hyperlink
4. Check "Highlight all items found ..."
5. Click on the Find All button
6. Close the dialog
7. Ctrl + C to copy everything that is highlighted
8. Open a new document and paste.

https://ccm.net/faq/25198-word-extract-all-hyperlinks-from-a-document