Creating a manual order with the “pay later” option would be the logical way to handle this situation but, as you’ve discovered, there doesn’t seem to be any way to create a draft order with Local Pickup as the option (nor change an order to local pickup after it’s created). This is obviously an omission and something you could ask Shopify to address (but realistically that's not likely to be a quick solution).
There are Apps that will do some of what you want. An example is Zapiet (no affiliation) which does have the concept of taking phone orders and will allow you to select Local Pickup after creating the order. However, this “Local Pickup” does not appear to be fully integrated with Shopify; only the App knows about the Local Pickup, so when I tried it, the order didn’t, for example, appear in the POS under “View orders to fulfil”, “Prepare for pickup”, “Send pickup notification” etc. I suspect other apps will have the same issue, but you could certainly take a look through the Shopify App store and maybe try a few - they might fit your needs.
The other option would be to simply enter the order through the Shopify front-end as if you were the customer. You’d be able to select Local Pickup and Pay on Collection (once you’d created that as a custom payment type), and the order would then likely do all the things you want it to in terms of standard Local Pickup management, notifications, POS integration etc.
As far as I'm aware, no app can integrate with Shopify's native Local Pickup feature.
However our app does allow you to add the customer's pickup details to a draft order. Zapiet - Pickup + Delivery also has its own notifications you can send to your customer (including one for when the order is ready for collection).
Our app has a 30 day free trial and 5 different levels of plan depending on your business' needs. If you'd like us to walk you through the setup and/or the workflow of managing your pickup orders, get in touch with us on email@example.com (or via the live chat module from inside our app once installed!)
Let me know if you have any further questions!
Bogi Szabo | Assistant Support Manager - Zapiet Ltd