Clearing your license information and doing the initial licensing procedure over again will do just fine. And that process is the correct one for leasing a Named CAL from your server, which is what you should do to fully license QlikView Desktop. After 28 days without contacting your QlikView Server, you will return to PE-mode.
BTW there is no such thing as an "Enterprise Edition" for a Desktop. Only a server license can be an Enterprise Edition license. Such a licnese will not work in QV Desktop.
A license key without control number = no license. The two cannot be separated.