My name is Lilith, I'm on the Social Care team at Shopify.
All of our free Shopify Themes allow you to enable this on your checkout. We have a great step by step guide in our Help Center if you've not had a chance to check it out.
The only free theme that won't do this out of the box is the Supply theme. I can't guarantee that paid themes all have this function available in their theme, but many of them will have various functions that could help with shipping customization notes. However, you can I highly recommend hiring one of our partners to help you add that to the Supply theme if that is the theme you would like to use. You can find a suitable Shopify Partner in the Experts Marketplace or request a quote by following this guide here.
Let me know how you do with the information above! I'm happy to answer any questions you think of as you work on your business.