The skin MediaMonkey uses can be changed under Tools > Options > Skin from the Main Menu. For skins to show the option to ‘Override Skin theme with Windows System theme (requires restart)’ needs to be disabled.

If after a MediaMonkey restart you still have the unskinned version of MediaMonkey running the link (MediaMonkey icon) you launch MediaMonkey with may be incorrect as the unskinned version of MediaMonkey runs from a different executable. Check the Properties of the link (MediaMonkey icon) you’re using and make sure it points to MediaMonkey.exe instead of MediaMonkey (non-skinned).exe.

The 2 executable for the skinned and unskinned versions of MediaMonkey can also cause the 2 icons for MediaMonkey to show. In that case just remove/unpin the icon you’re not using (points to the wrong MediaMonkey executable).