To use a courier without a mouse you should assign hotkeys, or a combination (for example, ALT + W) in Options. That will help you a lot during a fight.
Select Courier - switches from selected unit to the courier.
Courier Deliver Items - orders a courier to take your items from the stash and deliver to your hero.
Courier Speed Burst - increases courier's speed for a short time.
I usually use the following combination, four hotkeys: select courier (mouse additional button), collect items, deliver items and speed burst. Four keys to ask courier to deliver items fast.