As I cannot password protect the Zimbra offline store, the only way out is to protect the Windows Login Id.
In that case, can I use a different login Id on the same machine to have access to different email accounts. e.g. Family member 1 will use his Windows Login Id to access his yahoo accounts offline and Family member 2 will use her login id to access her yahoo account offline. This should happen in a way without interfering with each other's accounts or the offline store.