Here is a XAML only solution.
Just add this style to your button.
This will cause the context menu to open on both left and right click. Enjoy!
<Button Content="Open Context Menu">
<Button.Style>
<Style TargetType="{x:Type Button}">
<Style.Triggers>
<EventTrigger RoutedEvent="Click">
<EventTrigger.Actions>
<BeginStoryboard>
<Storyboard>
<BooleanAnimationUsingKeyFrames Storyboard.TargetProperty="ContextMenu.IsOpen">
<DiscreteBooleanKeyFrame KeyTime="0:0:0" Value="True"/>
</BooleanAnimationUsingKeyFrames>
</Storyboard>
</BeginStoryboard>
</EventTrigger.Actions>
</EventTrigger>
</Style.Triggers>
<Setter Property="ContextMenu">
<Setter.Value>
<ContextMenu>
<MenuItem />
<MenuItem />
</ContextMenu>
</Setter.Value>
</Setter>
</Style>
</Button.Style>
</Button>