Is there a module or way to edit all my product's categories from one admin menu?
Here are a couple of possibilities:


Perhaps try Views Bulk Operations - this might have an operation for changing taxonomy term in content in a batch.
If you are changing the same taxonomy term (old) to another term (new) on many products, I wonder if deleting the new term and then renaming the old term to what that new term was would do the job? The end result is that you now have products all using the new term. This idea would only be suitable if there isn't other content using that new term which is not part of the change.