How to load a content template part based on product-category in woo commerce

Hello,
I am using woo commerce (I know yours is good too :wink: and I am trying to do the following:
For all categories the woo commerce templates included in my themes are perfect.
For 1 category of product -rentals-, I'd like the content displayed (only the content part) slightly different.
I've duplicated the "content-single-product.php" into content-single-product-rentals.php" to get the appearance I'd like.
But I don't know how to call this template part.
1. Should I put something in my single-product.php to conditionally call the content part I want depending on the product-category? How can I do that?
2. Or should I create a redirection in the single-product.php

if( has_term( 'rentals', 'product_cat' ) ) {
    $file = 'single-product-rentals.php';
} else {
    $file = 'single-product-default.php';
}

global $woocommerce;

load_template( $woocommerce->template_url . $file );

> to a new single-product-rentals.php file which itself calls my content-single-product-rental.php ?

I guess it is a dumb question but I am just started with this.

Let me know,
Julien