Magic spells worked, magical equipment didn't. Kaldur's magical water weapons were completely useless.
I suppose completely disarming and handing a weapon over to your opponents COULD be a strategy, but they had enough information to know that it would have no effect beyond straight up handing their opponents your last weaponIn a fight like that, where there are so many unknowns, it can't hurt to attempt anything you can. The kryptonite ploy was worth the try.
On a show that wasn't as dependent on its heroes making mistakes, sure. Not this one, though.Also, don't be surprised if Nightwing actually planned for Zod to take his kryptonite from him. All may not be what it appears when it comes to a member of the Bat-family.
The Phantom Zone is inhumane and everybody in it needs to be rescued. They can be imprisoned or even executed afterwards but heroes that would leave people there for eternal torture are not heroes.