Disable Space Watching

For privacy/confidentiality concerns, it's not enough to be able to delete space watchers, we need to disable watching. We have a large enterprise and can't disable watching across the enterprise so we need to be able to completely disable watching on a space basis. Preferably configurable under Permissions or a simple check-box on Manage Watchers.

Stylesheet allows the removal of the Watch button for a space, but does not disable the shortcut (like removing buttons from the header does.) If there is something else we can remove using Stylesheet that would also be acceptable.