There is no key for autorun in Assassin’s Creed IV Black Flag (to always run, not having to press “shift”).
All you can do is to reassign the “shift” key to something else.
I’ve tried to reassign it to “space”, “q” or “e” but all seem to be even more uncomfortable to press than “shift”.
If your pinky hurts after pressing “shift” for too long, try pressing the button with your ring finger. The downside is that you can’t press “a” to strafe left. You can use the mouse to move the camera though.
A keypad like Razer Nostromo/Orbweaver/Tartarus is great here as you can assign shift to a lot of keys that are very comfortable to press.