Remove before_widget / after_widget content from Wp_Widget_Text

I want to take the text widget and remove the preceding / trailing markup from the text output currently showing as

<div class="textwidget">Test</div>

The before_widget / after_widget that is assigned with each widget area is under my control but the widget content itself is beyond me.

// Area 4, located in the footer. Empty by default.
    register_sidebar( array(
        'name' => __( 'First Footer Widget Area', 'lakeshoreautoclinic' ),
        'id' => 'first-footer-widget-area',
        'description' => __( 'The first footer widget area', 'lakeshoreautoclinic' ),
        'before_widget' => ' <p>',
        'after_widget' => '</p>',
        'before_title' => '<strong>',
        'after_title' => '</strong>',
    ) );

which outputs this for the surrounding / widget

<p><strong>Test</strong><div class="textwidget">Test</div></p>

You have a couple options as I see it:

There’s a the_widget() template tag that lets you control the before_widget and after_widget properties. However, it divorces the widget from the Widgets UI.

Alternately, you can try to accomplish whatever you’re trying to do via CSS. If you change your before_widget line to this:

'before_widget' => '<p id="%1$s" class="widget %2$s">',

you’ll get some classes and IDs that will make each widget style-able.