Like I said before forget anything but the wristlocks/cracks. Please read what i wrote: A martial art that revolves mostly around the oppoents attacks, close ranged COUNTER-attacks, as the opponent attack(kick,punch,stab,anything) crosses that personal defense line,when its close enough to grab/catch its arm/leg/any bodypart, and use his momentum to lose balance fall etc., forget anything besides the wristlocks.
I don't all the way understand what you're saying here, but I think you're saying that you've given up on the "no striking, no falling" criteria and are just looking for a style with no wrist locks?
For that, I would recommend a striking-only art, like Taekwondo or boxing. You'll learn how to counterattack and deal with close-range attacks by striking your opponent, and there won't be any joint locks.
But in a style where you learn to catch someone's arm and manipulate it so they fall, you're also going to have to the same thing done to you so your training partner can learn the techniques. And a joint lock is one of the best ways to manipulate someone's body and make them fall, so the curriculum will probably include them.