An example function that adds a 'Cancel Registration' option to the WP User integration add-on's 'My Events' section.

tw_ee_my_events_cancel_link.php

<?php

/* This function adds an icon to the 'My Events' section of the WP User intergration add-on which allows the user to cancel their registrations.
 * IMPORTANT NOTE - This function DOES NOT issue any refunds whatsoever, it simply changes the registration status to 'Cancelled' and triggers any related messages.
 *
 * It is HIGHLY recommended that you enable the 'Event Admin' context of the 'Registration Cancelled' message type:
 * Event Espresso -> Messages -> Default message templates -> Registration Cancelled -> Edit Event Admim
 * Make sure the context is active (the toggle switch) and that the TO field has a shortcode for the correct email to parse ( e.g [EVENT_AUTHOR_EMAIL] )
 * This way the event admin at least receives an email that shows the user cancelled their registration.
 *
 * The function checks for a custom value on each event with key 'allow_user_cancellations', set that to have any value and that single event will allow cancellations.
 * Use the filter below to allow cancellations on all events by default.
 */

// Uncomment this line to allow cancellations on all events.
// add_filter('AHEE__loop-espresso_my_events__allow_user_cancellations', '__return_true');

function tw_add_cancel_reg_to_my_events( $actions, $registration) {
    // Add a cancel registration link to my events.
    if ( $registration instanceof EE_Registration ) {
        if( $registration->status_ID() !== \EEM_Registration::status_id_cancelled &&
            (apply_filters('AHEE__loop-espresso_my_events__allow_user_cancellations', false) ||
            get_post_meta( $registration->event_ID(), 'allow_user_cancellations', true)) 
        ) {
            $query_args = array(
                'ee_cancel_registration' => $registration->ID(),
            );
            $cancel_reg_url = esc_url(add_query_arg( $query_args ));
            $cancel_reg_text = __( 'Link to cancel registration', 'event_espresso' );
            $actions['cancel_reg'] = '<a aria-label="' .  $cancel_reg_text
                . '" title="' . $cancel_reg_text
                . '" href="' . $cancel_reg_url . '">'
                . '<span class="dashicons dashicons-dismiss ee-icon-size-18"></span></a>';
        }
    }
    return $actions;
}
add_filter( 'FHEE__EES_Espresso_My_Events__actions', 'tw_add_cancel_reg_to_my_events', 10, 2);
function tw_add_cancel_reg_to_my_events_legend( $items ) {
    // Add the cancel registration icon to the legend.
    $items['cancel_reg'] = array(
        'class' => 'dashicons dashicons-dismiss',
        'desc' => esc_html__( 'Cancel registration', 'event_espresso' )
    );
    return $items;
}
add_filter( 'FHEE__status-legend-espresso_my_events__legend_items', 'tw_add_cancel_reg_to_my_events_legend');

function tw_ee_cancel_reg_from_my_events($object_type, $objects, $template_slug, $att_id) {
    if( empty($att_id) || $att_id != get_user_option('EE_Attendee_ID', get_current_user_id()) ){
        // For whatever reason, the att_id is not set or doens't match the value from the current user,
        // Return and do nothing as we want to be sure we are only cancelling regs linked to the current user.
        return;
    }
    // Get the REG ID passed from my events.
    $loader = EventEspresso\core\services\loaders\LoaderFactory::getLoader();
    $request = $loader->getShared('EventEspresso\core\services\request\Request');
    $REG_ID = $request->getRequestParam('ee_cancel_registration');
    // Get out if no REG_ID
    if(empty($REG_ID)) {
        return;
    }
    // Pull the registration using the ID passed.
    $registration = EEM_Registration::instance()->get_one_by_ID($REG_ID);
    // Check we have a valid registration.
    if( $registration instanceof EE_Registration &&
        $registration->status_ID() !== \EEM_Registration::status_id_cancelled &&
        (apply_filters('AHEE__loop-espresso_my_events__allow_user_cancellations', false) ||
        get_post_meta( $registration->event_ID(), 'allow_user_cancellations', true ))
    ) {
        // Pull the attendee linked to the registration.
        $attendee = $registration->attendee();
        // Confirm that the attendee linked to the registration in question has the same ID as the attende linked to the user.
        if( $attendee->ID() == $att_id ) {
            //Set the registration to cancelled.
            $registration->set_status( \EEM_Registration::status_id_cancelled );
            // Trigger notifications.
            $registration_processor = \EE_Registry::instance()->load_class('Registration_Processor');
            add_filter('FHEE__EED_Messages___maybe_registration__deliver_notifications', '__return_true', 10);
            $extra_details = array(
                'finalized' => true,            
            );
            $registration_processor->trigger_registration_update_notifications($registration, $extra_details);
            // Add notice showing the registration has been cancelled.
            EE_Error::add_success(
                esc_html__('The selected registration has been cancelled.', 'event_espresso')
            );
            EE_Error::stashNoticesBeforeRedirect();
            // Redirect back to 'My Events' to prevent multiple notifications.
            wp_safe_redirect($_SERVER['HTTP_REFERER']);
            exit();
        }
    }
}
add_action( 'AHEE__loop-espresso_my_events__before', 'tw_ee_cancel_reg_from_my_events', 10, 4);