ETA: This will disable the software (you can still re-enable at a future point), not just stop the menu from coming up. For a more nuanced solution, see Synycalwon's directions below.
Samsung Galaxy Note 4 - How to turn off the Air command feature
To turn off the Air command feature of the Samsung Galaxy Note 4:
Go to Settings > Controls.
Tap on S Pen
Tap on Air Command
Disable Air Command.