ToolTip is hosted inside a Popup which in turn is rendered in a separate HwndSource, you should be able to mimic the ToolTip behaviour using Poup, and set its StaysOpen property to true as the following XAML illustrates:

<Page xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml">
<
Button Width="120" Height="30" Name="btn">
<
Popup IsOpen="True" StaysOpen="True" PlacementTarget="{Binding ElementName=btn}" Placement="Bottom">
<
Button Width="120" Height="30" Content="Button In ToolTip"/>
</
Popup>
</
Button>
</
Page>