I just wasted 3 hours of my life trying to set this value in xml.
Normally you think that in a Block when you see $this->getChildrenWrapClass() that the value for that would come from xml or in an observer where that value is being set by $block->setChildrenWrapClass(), however for this you would be totally mistaken.
<reference name="catalog.topnav.renderer">
<action method="setData"><name>setChildrenWrapClass</name><value>abc123</value></action>
<action method="setData"><name>children_wrap_class</name><value>321cba</value></action>
<action method="setChildrenWrapClass"><value>ecreameryTest</value></action>
</reference>
That was all the different types of xml I was trying to use to get that value set!
Well, it turns out this is actually a parameter that is passed into getHtml()
Sigh