You can achieve this by following the steps below to enable manual payment and disable the buy buttons.
Manual Payment
Navigate to store Settings and select Payments. Under Manual Payment Methods click +Manual Payment Method and select Create Custom Payment Method. This will enable a new payment option during checkout, with the customer still being required to input their information.
Remove buy button
Go to Online Store, Customize and select Products from the drop down menu at the top of the screen. Click Buy buttons in the left hand menu and over on the right deselect Show dynamic checkout buttons. This will disable the buy now buttons, leaving only the add to cart option.
The order will still be created as normal, but you wil have the option to invoice the customer, and mark as payment received/dispatched etc accordingly.
Hope this helps
Simon