Acrobat offers the batch/Actions sequences, where it would be possible to get rid of actual hyperlinks. However, if you talk of thousands of files, Acrobat may not be stable enough, and you would need something more industrial size.
I think there is a product by Appligent which does remove annotations (and Links are annotations); contact them and ask. This would be a command line tool, which can easily be included in a script for your operation system.
If you nevertheless want to do it in Acrobat, you would create a sequence, and you should be able to use the PDFOptimizer to clean up your documents.
Hope this can help.