Cannot set cash as payment option for local client

Hi,

That's not a problem. Go in the menu System>Payment methods and click on the "new" button. There, select the "collect on delivery" payment method, that you can potentially rename 'pay by cash at the store' based on what you want to display to the customers.
That way, the customers will be able to select that payment method on the checkout, you'll get the email notification and order in your website, and when the customer comes in with the cash, you can just change the order status in the backend of the website.