Is there a way to hook or call a custom woocomerce template that is not part of the default templates of woocommerce?

You could consider using the good ol’ get_template_part( string $slug, string $name = null, array $args = array() function, which is a native WP function. Especially now as it supports the third parameter for passing data to the template file (since WP 5.5).

Create a function (in your (child) theme functions.php file) that wraps around some get_template_part() call and hook it onto suitable action that WooCommerce provides.

https://developer.wordpress.org/reference/functions/get_template_part/

EDIT 30.8.2020

You could for example have the following structure in your (child) theme directory,

/my-child-theme
--/parts
----/my-template-part.php
----/my-template-part-alt.php

To use the custom template parts, you could do the following in your functions.php file.

add_action( 'some_woocommerce_template_action', 'my_fancy_template_part' );
function my_fancy_template_part() {
    // pass data to the template part in an array
    $args = array(
        'key_1' => 'foo',
        'key_2' => 'bar',
    );
    get_template_part( '/parts/my-template-part', null, $args );
}

add_action( 'some_other_woocommerce_template_action', 'my_fancy_template_part_alternative' );
function my_fancy_template_part_alternative() {
    // get a "named" part with shared prefix
    get_template_part( '/parts/my-template-part', 'alt' );
}

If you passed $args as the third parameter to get_template_part(), you can the access them in your template part file like so,

echo $args['key_1']; // foo

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