Hi @allgoodnamesaretaken!
You can find all the available snippets of WooCommerce for you to use here:
https://woocommerce.com/documentation/woocommerce-codex/snippets/
Since hiding the add to cart button isn’t a core feature of WooCommerce, you can achieve it through a plugin or custom coding.
Searching, I found a plugin that could be useful to your case:
https://woocommerce.com/products/hide-price-add-to-cart-button/
Also found an article that seems to have the code you need:
https://wisdmlabs.com/blog/the-right-way-to-hide-add-to-cart-button-in-woocommerce/
Kindly notice that since custom coding is outside our scope of support, for additional assistance on this topic, we recommend getting in touch with one of the customization experts listed on the WooCommerce Customizations Page.
Also, if you are into coding, you can visit the WooCommerce Facebook group or the #developers channel of the WooCommerce Community Slack, you could find help from the community of open-source developers for WooCommerce that hangs in there.
Cheers!