I have recently been working on a WPF touch screen application that doesn’t lend it self well to normal scroll bars. Luckly this is no problem with WPF because you have the ability to easily modify how a control is rendered. Below is a rough template that puts a button above and below scrollable content and when clicked they provide the same functionality as the default scroll bar.
<ControlTemplate TargetType="{x:Type ScrollViewer}"
x:Key="ButtonOnlyScrollViewer">
<Grid>
<Grid.RowDefinitions>
<RowDefinition Height="Auto"/>
<RowDefinition Height="*"/>
<RowDefinition Height="Auto"/>
Grid.RowDefinitions>
<Grid.ColumnDefinitions>
<ColumnDefinition />
<ColumnDefinition />
Grid.ColumnDefinitions>
<RepeatButton Grid.Row="0" Grid.Column="0" HorizontalAlignment="Stretch"
Content="ScrollUp"Command="ScrollBar.LineUpCommand"/>
<ScrollContentPresenter Grid.Row="1" Content="{TemplateBinding Content}"
Grid.Column="0" ScrollViewer.VerticalScrollBarVisibility ="Auto"
Height="Auto" Margin="{TemplateBinding Margin}"/>
<RepeatButton Grid.Row="2" Grid.Column="0" Height="20"
Content="ScrollDown"
Command="ScrollBar.LineDownCommand"/>
Grid>
ControlTemplate>