I agree on it looking like a very fun idea.
Regarding how it'd work, you'd need to add a new equipment filter/category for "non-lethal", and also give a metric fuckton of negative points for killed enemies.
If "enemies" also have only non-lethal weaponry, the only way to explain why squad wipes (everyone falling uncoscious) are possible is that their performance was so bad they were fired by the council as a political way to save face, regardless of their history and stats. And for this reason, no mission aborting - it wouldn't make sense to let those who managed to flee keep their job.
Regarding rewards, besides points, I'm thinking the biggest draw should be a commendation, with more stats rewards than usual, acting as a training certificate. Maybe each soldier could only get one level of such certification max, but there could be multiple different certifications for multiple different training exercices, be they differing in difficulty/tier or in ambit: rescue and fire-fighting, finding and capturing a dogs (trained not to bite) in a limited number of turns...
But yeah, this is extra work, and as much as I'd love it, I'd rather you invest developement time into finishing cult of apocalypse and MiB.