This isn't really a setting, but rather permissions. What the wizard does, is assigning the required permissions required to join a computer to that computer-object on the object for the user/group that you specified.
Usually what people do is adding a user to a ADgroup which has the required permissions to join computers; permissions being assigned on a parent container of the computers with inheritance enabled.
If you need to make only THAT person be able to join THAT computer, you would need to script it. Ex:
- Create a computer-object and choose a specific user in the wizard.
- Use ADSI or Powershell etc. to export the ACLs created for the specified user on that computer object
- Create a script that assigns the same permissions for a specified user on a specified computer.