Hi,
When a payment via a payment gateway (like PayPal, Stripe, etc) is received for an order, the payment plugin will trigger the sending of an email to the customer for his payment. This will happen regardless of the "Send Details Of The Order" setting. It only depends on whether you've disabled or not the "order status notification" email via the System>Emails menu.
Usually, the status of an order being changed to "shipped" happens when the merchant manually changes the status of the order in the backend of the website. When he does so, there is a checkbox he can check to send an email notification to the customer. If that checkbox is checked, the "order status notification" email will be sent, provided it has not been disabled.
So, what you're asking for should already be happening, unless you don't check the "notify user" checkbox when you change the status of an order to "shipped" in the backend of HikaShop.