Magento 1.9 – Search Filter Not Working

I don't know how your extension is built, so I cannot provide any code but here is an idea on wow you can do it.
In a search page this piece of code will return null always:

Mage::registry('current_category');

In a category page this will return a category instance. You can use this in your own block. So for each method you override you can do the followin check before doing something. Let's say your method is called doSomething(). In your block it could look like this:

public function doSomething($someParam) {
    if (!Mage::registry('current_category')){//not on category page
        //call the default behavior
        return parent::doSomething($someParam);
    }
    //your custom behavior here
}

You can even change the template that renders the block this way:

public function __construct()
{
    parent::__construct();
    //by default the template 'catalog/layer/filter.phtml' will be set
    if (Mage::registry('catalog_category')){//if category page
        //set your custom template with price slider.
        $this->setTemplate('custom/template/here.phtml');
    }
}

Add the following node to local.xml file of your theme:

<catalogsearch_result_index>
    <reference name="catalogsearch.leftnav">
        <action method="unsetChild"><name>category_filter</name></action>
    </reference>
</catalogsearch_result_index>