Hello,
As you are probably aware, KonaKart has a modular architecture so that shipping modules can be easily added or removed. To solve your problem, I think that you could use the Cash on Delivery module that we already supply, by just changing the wording so that it doesn't say Cash on Delivery on the UI. This module allows a user to enter an order and complete the checkout process without paying for it.
When someone comes to one of your shops to pay, you can change the status of the order through the admin app to identify that it has been paid. Also you could use a couple of the custom fields on product object to keep the stock level present in each branch. It would be the responsibility of the shop owner to decrement the quantity (through the Admin App) every time a customer comes in to pay.
Let me know if this solution could solve your problem.
Thanks,
Paolo