Is there a way to add a button to a video in woo product grid?

Not sure about plugins. But what I can think of is to use custom code in child theme functions.php, using this hook: woocommerce_after_shop_loop_item

Example:

Code:

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The above code will inject 'Your Text' below all your loop products. To achieve what you want, you will need custom field for the Woocommerce for the video link & use the above code to inject the 'watch video' button with the custom field link.

You might want to search stackoverflow for sample code regarding: woocommerce_after_shop_loop_item