Hi Chris,
You can create a general user and only add the user to local group "Users" in PC/Laptop, and then deny group "Users" to create file or directory on local PC.
Image may be NSFW.
Clik here to view.
After you complete these settings ,use the general user as credential to log into local PC/Laptop, and then prefer to the link below to map SharePoint Online library to a network driver:http://support.microsoft.com/kb/2616712
The general user would only be able to save data in SharePoint Online library.
This is only workaround for your reference.
Thanks,
Jacky Ding