When I try to do a non-lethal takedown the normal way (sneaking up behind the enemy and pressing the takedown button) against an enemy in an exosuit, the attack just bounces off the exosuit, doing no damage and alerting the enemy to my presence. How do I do a non-lethal takedown of an enemy in an exosuit without breaking stealth?
To perform a non-lethal takedown of an enemy in an exosuit, you must stun the enemy first with an EMP weapon (e.g. gun with EMP ammo, stun gun, EMP grenade). After stunning the enemy, you can perform the takedown the way you do with other enemies -- by sneaking up behind them an pressing the takedown button.
If the weapon you use to stun the enemy is silenced, or if you're far enough from other enemies that they will not hear the weapon, your stealth should be maintained.