One way is to change RadMediaPlayer's ControlTemplate thus removing the controls.
The other way is much shorter. As soon as the Page loads, you can set the RadMediaPlayer.IsFullScreen to true. This way, every time the user enters RadMediaPlayer with his/her mouse the controls will appear. As soon as he/she leaves, the controls will disappear.
I have created a sample project demonstrating this functionality. Have a look at it and let me know how it works for you.
the Telerik team