A generic toggle control you can use to replace the checkbox control.

I've added this control to my customizer demo theme.

Clone this repository and include the class:

/**
 * Check for WP_Customizer_Control existence before adding custom control because WP_Customize_Control
 * is loaded on customizer page only
 *
 * @see _wp_customize_include()
 */
if ( class_exists( 'WP_Customize_Control' ) ) {
	require_once( dirname(__FILE) . '/class-customizer-toggle-control.php' );
}

$wp_customize->add_control( new Customizer_Toggle_Control( $wp_customize, 'my_control', array(
		'label'	      => esc_html__( 'Toggle me on or off', 'my-lang' ),
		'section'     => 'my_section',
		'settings'    => 'my_setting',
		'type'        => 'ios',// light, ios, flat
) ) );

Three different types are available

You must update the js/customizer-toggle-control.js file if you want to change the title color when a toggle is disabled/enabled.

The CSS is copyright (c) 2016 by Mauricio Allende

You can see his demo at CodePen.io

The CSS is licensed under the terms of the MIT license

WordPress Customizer Toggle Control is copyright 2016 Per Soderlind

WordPress Customizer Toggle Control is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 2 of the License, or (at your option) any later version.

WordPress Customizer Toggle Control is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with the Extension. If not, see http://www.gnu.org/licenses/.