If you modify the style in Expression Blend of the RadUpload control, you will see several VisualStates in Upload's control template. For example, the state when there are selected files looks like this:
These animations control the visibility of all the buttons in the upload control. You should set the value of the discrete frames to Collapsed on the buttons that you do not want to be visible in all of the states and apply the style to the upload control.
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