Manual:$wgSkipSkins

Details
Specify the names of skins that should not be presented in the list of available skins. Use for blacklisting one ore more skins which you do not want to remove from the  directory

Example, in LocalSettings.php put: Above would remove all skin choices but monobook. If you want to remove Classic, include 'standard' in the above array. Omit from above array any choices that you want to remain.