EDIT: Hang on, I’ll do some more details..
First, we know that you may not delete a category unless it is emtpy (nothing but the category definition).
You usually don’t want to delete all the topics, so move them to another existing category instead. In this case, move them to the category that’s the “target” of the merge.
The bulk actions is a good way to easily change the category of all of them.
Once you’ve moved them all out, you can delete the category. You’ll need everybody to refresh afterwards.