The cats conquer the balcony

This spring a family of squirrels moved into the unkempt balcony next door.
Normally the cats are let out on the balcony with a supervisor close by as they like the fresher air and the myriad animals they can stare at.
However with the new family moved in next door the cats were much more interested in the other balcony and were doing whatever it would take to get over there.
I have already proofed the balcony so that the cats are not able to go visit the neighbors as once Johnny went over and just went into their apartment and apparently freaked them right out.
But - this time the squirrels decided to come over and visit and be aggressive with the cats. Johnny and Gloom Cookie were of coursed thrilled with this. They wanted to fight them, beat them up, catch them, you know cat stuff.
Monster Squad slid a note under the neighbors door asking them to take care of the pesky problem. And they did clean up their balcony and remove the hiding places for the squirrels, however, they did not go away.
And this morning Johnny was feeling extra feisty and managed to catch and kill one of them and wanted to bring it to me to show me.
Thank you, but no.
Monster Squad was traumatized and I was the one responsible for taking the fresh kill away from Johnny and then disposing of it. And I am now worrying about the possibility of some disease transmission. But cats kill birds all the time and bring them home so hopefully this is not a big deal. (I am actually kind of impressed that Johnny had the skills to catch and kill this animal - he is a bit of a doofus at times).
So hopefully with the cats following their instincts this means that the squirrels will stay away. Or another one may get it.