>> two of these VMs are clustered with iSCSI bus sharing between them. Is it possible to move them one by one and avoid downtime for the applications? Or will I have to shut them down both and register them both to the vCenter before turning them on?
Safest way is to shutdown both the VMs based on what application is being configured between these VMs and register both of them into 6.7U2 vcenter.
There should not any issue from VM hadrware version compatibility perspective , refer KB VMware Knowledge Base