Manual:$wgSkipSkins

Details
Specify the names of skins that should not be presented in the list of available skins.

Use for preventing users from choosing one or more skins which you do not want to remove from the  directory.

Example, in LocalSettings.php put:

Above would remove all skin choices but Vector. Omit from above array any choices that you want to remain.

Changing user preferences when removing a skin
<!- the skin