Once you have ShipStation's Advanced Hotkeys and their scannable barcode equivalents set up, it is possible to completely fulfill an order without ever using a mouse.
First, you'll want to go to the orders page by using the Go to Orders hotkey by pressing g then o.
On the Orders page, you can use your keyboard directional keys to navigate through your orders. To Move to the next row press the ▼ key or to Move to the previous row press ▲.
Pressing v will let you View Order Detail window for the selected order. On the Order Detail window, the ► key will Move to the next Order Details window. Likewise, the ◄ key will Move to the previous Order Detail window.
When you have the order you need to ship selected, apply the desired Shipping Preset to apply the shipment details like package type and weight. These hotkeys are completely configurable, and will have a barcode equivalent like all other hotkeys.
Now, in order to ship this order mouse-free, you'll need to toggle Quickship on by pressing q. Create Label(s) must be orange to print via Advanced Hotkeys or barcode functions.
Press s to create the label, and your shipment will be generated!