Try like this:
if (control.ToolTip != null)
{
    // Main condition
    if (control.ToolTip is ToolTip)
    {
        var castToolTip = (ToolTip)control.ToolTip;
        castToolTip.IsOpen = true;
    }
    else
    {
        toolTip.Content = control.ToolTip;
        toolTip.StaysOpen = false;
        toolTip.IsOpen = true;
    }
}  
The Main condition necessary, because ToolTip for Control can be set in two approaches:
First approach 
<Button Name="TestButton"
        ToolTip="TestToolTip" />
This approach is most common. In this case, the content of the ToolTip will object and not type of ToolTip.
Second approach
<Button Name="TestButton"
        Content="Test">
    <Button.ToolTip>
        <ToolTip>TestToolTip</ToolTip>
    </Button.ToolTip>
</Button>
Is the same as this:
<Button Name="TestButton"
        Content="Test">
    <Button.ToolTip>
        TestToolTip
    </Button.ToolTip>
</Button> 
In this case, the Content type of ToolTip will be Tooltip. Note that in the second case, the object automatically fills ToolTip object on line TestToolTip, hence this approach will work a bit slower.
Therefore, this check is needed to avoid an exception when we try to assign to the ToolTip the content of the ToolTip type here:
toolTip.Content = control.ToolTip;
Below is a full example:
XAML
<Grid>
    <Button Name="TestButton"
            Width="100"
            Height="25"
            Content="Test" 
            ToolTip="TestToolTip" />
    <Button Name="ShowToolTip" 
            VerticalAlignment="Top"
            Content="ShowToolTip" 
            Click="ShowToolTip_Click" />
</Grid>
Code-behind
public partial class MainWindow : Window
{
    public MainWindow()
    {
        InitializeComponent();
    }
    private void ShowToolTip_Click(object sender, RoutedEventArgs e)
    {
        var toolTip = new ToolTip();
        if (TestButton.ToolTip != null)
        {
            if (TestButton.ToolTip is ToolTip)
            {
                var castToolTip = (ToolTip)TestButton.ToolTip;
                castToolTip.IsOpen = true;
            }
            else
            {
                toolTip.Content = TestButton.ToolTip;
                toolTip.StaysOpen = false;
                toolTip.IsOpen = true;
            }
        }  
    }
}