You can achieve your requirement using the Shipping option of WooCommerce which doesn't require the specific setting in the plugin to allow selecting either delivery or pickup option.

For this, kindly follow the below steps:
1. Set the "Pickup" and "Delivery" shipping methods in WooCommerce > Shipping section.
At backend:

2. Create Custom Delivery Date Setting based on shipping method from our Order Delivery Date plugin where you can set different delivery date field names with different delivery dates and time settings.

Screenshots for Delivery option: , ,

Screenshots for Pickup option: , ,

Thus, if the customer will select "Pickup" Shipping method, the setting of the "Pickup" will be loaded and if the customer will choose "Delivery" option then the setting of "Delivery" will be loaded.

For detailed information, please refer to this documentation