Disable Offline Files on a subfolder

Is there any way to disable offline files on an individual subfolder of "Documents"?  We had a situation where a staff member lost their laptop and had sensitive student information saved in a folder inside "Documents".  We are looking for a way to prevent this from happening again.  We could have them save to a network share but first want to see if disabling offline files for a specific subfolder was possible.

Thanks

me