Unfortunately, there's no easy way to do this. Ideally, you'd set ToolTipService.InitialShowDelay on FrameworkElement and let it propagate from there, but it turns out that doesn't seem to work.
Instead, you can set it on each type of control you want to set it on, for instance:
<Style TargetType="RibbonButton">
<Setter Property="ToolTipService.InitialShowDelay" Value="2000"/>
</Style>
<Style TargetType="RibbonToggleButton">
<Setter Property="ToolTipService.InitialShowDelay" Value="2000"/>
</Style>
<Style TargetType="RibbonDropDownButton">
<Setter Property="ToolTipService.InitialShowDelay" Value="2000"/>
</Style>
etc.
Although this is a pretty verbose way of doing it, at least you only have to set it on each type of control and not every control itself - and if you're using it in the Ribbon, then there's only a handful of controls to begin with.
To save yourself some hassle should you ever want to change the value, you may want to architect the above code using a resource value:
<sys:Int32 x:Key="ToolTipInitialShowDelay">2000</sys:Int32>
<Style TargetType="RibbonButton">
<Setter Property="ToolTipService.InitialShowDelay"
Value="{StaticResource ToolTipInitialShowDelay}"/>
</Style>
<Style TargetType="RibbonToggleButton">
<Setter Property="ToolTipService.InitialShowDelay"
Value="{StaticResource ToolTipInitialShowDelay}"/>
</Style>
<Style TargetType="RibbonDropDownButton">
<Setter Property="ToolTipService.InitialShowDelay"
Value="{StaticResource ToolTipInitialShowDelay}"/>
</Style>
Alternatively, if you are not already using BasedOn styles, you could shorten it to:
<Style x:Key="ToolTipDefaults">
<Setter Property="ToolTipService.InitialShowDelay" Value="2000"/>
</Style>
<Style TargetType="RibbonButton" BasedOn="{StaticResource ToolTipDefaults}"/>
<Style TargetType="RibbonToggleButton" BasedOn="{StaticResource ToolTipDefaults}"/>
<Style TargetType="RibbonDropDownButton" BasedOn="{StaticResource ToolTipDefaults}"/>
The limitation to this approach being that a style can only be based on one parent style, so if you're already using this pattern, you won't be able to do this.