Not sure about deleting all the local files - as I keep mine as backup.
I use S3:
Admin->CDN->Host Attachment. Make sure that is checked and click on 'Upload Attachment'. (Assuming you have the CDN credentials set in the settings)
And the site does not reference any local files - so in theory, if I delete my local files, it should work.
There is also 'Importing attachments into the Media Library' on the same page, if you are doing it for the first time.