Thank you for reaching out.
First, congratulations on your first order!
I understand your customer wants to change the delivery method on their order to local pickup. Just to confirm, are you looking to remove/refund the shipping fee?
There isn't a way to change the delivery method after the customer has finalized their order. However, if you're communicating with the customer, you can inform them and refund the shipping fee portion of their order. That being said, to also protect yourself from any potential charge disputes, I'd recommend keeping the conversations with your customer to account for the partial refund on their order.
As another option, you can refund the original order and create a draft order with the changes to their order. Then, you'll be able to send the new invoice to your customer and re-capture the payment. This method is recommended, as it doesn't require referencing separate orders or handling partial refunds.
I hope this helps! If you have any other questions on this topic, please don't hesitate to let me know!