My suggestion would be just this… except the unchecking step can be easier. Instead of manually clicking on each item you can:
Select entire document.
Command-T (Tag With…) and then choose a tag. That will either add or remove the given tag from all selected items. So do it once or twice and that tag should be removed.
If you’d like some other workflow you can automate it via scripting. Can get quite complex! This page includes lots of user shared scripts:
And this script in particular might be of interest: