Use Caps Lock to hold the Shift key down in Minecraft
This runs as a Tray Icon (the icons by the clock). When you have CapsLock turned on while in Minecraft, it will press Shift for you. You can release shift by turning CapsLock off. It also attempts to tell when you are in chat, so you don't have to worry about screaming at people in chat.
Inspired by u/Nacoran on Reddit and the comments under his suggestions