Hacky solution:
put a "transparent" rectangle in the same place, and make your rectangle IsHitTestVisible="False"
<Rectangle x:Name="Clickable"
Grid.Column="1"
MouseUp="HandleMouseUp"
Fill="#01FFFFFF"/>
<Rectangle Grid.Column="1"
Stroke="Red"
StrokeDashArray="4.0 4.0"
StrokeThickness="{Binding Path=CurrentThickness}"
IsHitTestVisible="False"
Visibility="{Binding Path=VisibleRectangle,
Converter={StaticResource VisibilityConverter}}"/>