Hi Brent,
I am sure that you will understand, this is a customization request and outside of our support scope. But we will do our best to get you started with the customization, the rest is on your shoulders.
I suggest that you consider going about the translation route. Most of the good plugins allow the translation of the auto-generated text and you can make use of it to change the Shipping to Delivery.
You can check our documentation for our theme generated text:
Here is more information on how to translate the Woocomemrce plugin:
In the custom translation mentioned in the article above you will need to change Shipping to Delivery. So the basic idea is that you do not translate to another language, and you translate to your desired wording.
If you use third-party plugins that they might also have generated text for the Shipping, you need to read their documentation on how to translate the plugin. The concept is the same though.
Thank you.