
If the style names are identical in the new and old designs, you should be able to update the styles by attaching a new template to the documents:
- Open a document in the old format.
- Choose File>Options>Add-ins.
- Set the Manage dropdown to Templates, then click on the Go button.
- Check the Automatically update document styles check box.
- Click on the Attach button and find the new template. Select it and click on the Open button.
- Close the dialog and save the updated document.
- Repeat steps 2 and 3.
- Uncheck the Automatically update document styles option. OK out and resave.
It would be possible to automate the conversion using VBA macros. It's not a beginner project.